Options and Derivatives
1. What is an exchange?
An
exchange, refers to a marketplace or platform where various financial
instruments, such as stocks, bonds, commodities, derivatives, and currencies,
are traded. It provides a centralized venue where buyers and sellers can come
together to execute transactions.
Exchanges
play a vital role in facilitating the smooth functioning of financial markets
by providing a transparent and regulated environment for trading. They
establish the rules, regulations, and procedures that govern the trading
activities, ensuring fair and orderly markets.
2. What is over the counter market?
The over-the-counter (OTC) market refers to a decentralized marketplace where financial instruments, such as stocks, bonds, derivatives, and currencies, are traded directly between two parties without the involvement of a centralized exchange. In contrast to exchange-traded markets, OTC markets are typically less formal and operate through a network of dealers and brokers.
3. What is a Derivative?
In finance, a derivative is a financial instrument whose value is derived from an underlying asset or set of assets. The underlying asset can be a commodity, stock, bond, currency, or an index. Derivatives are used as a way to manage and mitigate financial risk or to speculate on future price movements.
Derivatives play a crucial role in financial markets, allowing investors, traders, and institutions to manage risk, hedge against price movements, speculate on future prices, and enhance investment strategies. However, it’s important to note that derivatives can also involve higher levels of risk and complexity compared to traditional investments.
4. What are different types of Derivatives traded in the market?
Derivatives in finance can be classified into four main types:
a) Forwards: Forwards are contracts but are customized agreements between two parties rather than standardized contracts traded on OTC. They specify the price and delivery date for the underlying asset. Forwards are commonly used in over-the-counter (OTC) transactions, allowing parties to tailor the terms of the agreement to their specific needs.
b) Futures Contracts: Futures contracts are agreements to buy or sell an asset at a predetermined price and date in the future. They are standardized contracts traded on exchanges and are commonly used to hedge against price fluctuations. For example, a farmer might enter into a futures contract to sell their crop at a fixed price in order to protect against a drop in prices.
c) Options: Options give the holder the right, but not the obligation, to buy (call option) or sell (put option) an asset at a predetermined price within a specified period. Options provide flexibility and can be used for hedging, speculation, or generating income. Traders can use options to protect their portfolio against downside risk or to leverage their investment.
d) Swaps: Swaps are agreements between two parties to exchange cash flows based on predetermined terms. The most common type of swap is an interest rate swap, where two parties agree to exchange fixed and floating interest rate payments over a specified period. Swaps are used to manage interest rate risk, currency risk, or to modify the cash flow characteristics of assets or liabilities.
5. How exchange plays an important role in future contract?
Suppose, for example, that trader A agrees to buy 100 ounces of gold from trader B at a future time for $1,250 per ounce. The result of this trade will be that A has a contract to buy 100 ounces of gold from the clearing house at $1,250 per ounce and B has a contract to sell 100 ounces of gold to the clearing house for $1,250 per ounce. The advantage of this arrangement is that traders do not have to worry about the creditworthiness of the people they are trading with. The clearing house takes care of credit risk by requiring each of the two traders to deposit funds (known as margin) with the clearing house to ensure that they will live up to their obligations.
6. What is forward contract?
A forward contract is an agreement to buy or sell an asset at a certain future time for a certain price. A forward contract is traded in the over-the-counter market—usually between two financial institutions or between a financial institution and one of its clients.
One of the parties to a forward contract assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. The other party assumes a short position and agrees to sell the asset on the same date for the same price.
7. What are payoffs from forward contract?
Payoff from a long position (buyer) = ST – K
Payoff from a short position (seller) = K – ST
where K is the delivery price and ST is the spot price of the asset at maturity of the contract.
8. Can you draw the payoff for forward contract for long position and short position?
Payoff from a long position (buyer) = ST – K
Payoff from a short position (seller) = K – ST
9. Can you tell the specifications of a future contract?
A futures contract is a standardized agreement between two parties to buy or sell a specified asset (referred to as the underlying asset) at a predetermined price (referred to as the futures price) and on a specific future date (referred to as the expiration date). Here are the key specifications of a futures contract:
a) Underlying Asset: The futures contract specifies the type of asset that is being traded. It can be commodities (such as crude oil, gold, wheat), financial instruments (such as stock indices, currencies), or other assets.
b) Futures Price: The futures price, also known as the strike price or exercise price, is the pre-agreed price at which the underlying asset will be bought or sold upon contract expiration. It is determined at the time of entering the contract.
c) Contract Size: The contract size, also known as the lot size, represents the quantity or amount of the underlying asset that is covered by a single futures contract. It defines the standard quantity that will be bought or sold upon contract expiration.
d) Expiration Date: The expiration date is the date on which the futures contract expires. After this date, the contract is no longer valid, and any open positions need to be settled or rolled over to a new contract if desired.
e) Price Quotes The exchange defines how prices will be quoted. For example, crude oil futures prices are quoted in dollars and cents. Treasury bond and Treasury note futures prices are quoted in dollars and thirty-seconds of a dollar.
f) Tick Size: The tick size refers to the minimum price increment or the smallest price movement allowed for the futures contract. It varies depending on the underlying asset and is set by the exchange.
g) Delivery/Settlement: Futures contracts can be settled in two ways: through physical delivery or cash settlement. Physical delivery means that the buyer receives the actual underlying asset upon contract expiration, while cash settlement involves the transfer of cash based on the contract’s value at expiration.
h) Delivery Months: A futures contract is referred to by its delivery month. The exchange must specify the precise period during the month when delivery can be made. For many futures contracts, the delivery period is the whole month. For example, corn futures traded by the CME Group have delivery months of March, May, July, September, and December. At any given time, contracts trade for the closest delivery month and a number of subsequent delivery months.
i) Exchange and Clearinghouse: Futures contracts are traded on organized exchanges, such as the Chicago Mercantile Exchange (CME) or Intercontinental Exchange (ICE). These exchanges provide a centralized marketplace for trading futures contracts. A clearinghouse acts as a middleman, facilitating the clearing and settlement process between buyers and sellers.
10. Who are hedgers, speculators, and arbitrageurs?
Hedgers, speculators, and arbitrageurs are three distinct types of market participants, each with different objectives and strategies:
Hedgers:
- Hedgers are market participants who use financial instruments, such as futures contracts or options, to manage or mitigate their exposure to price volatility or risk. They aim to protect themselves from adverse price movements in an underlying asset by taking offsetting positions in the derivatives market.
- For example, a farmer who anticipates selling a crop harvest in the future may use futures contracts to lock in a price in advance, protecting against potential price declines.
- Similarly, a multinational corporation with foreign currency exposure may use currency derivatives to hedge against exchange rate fluctuations.
Hedgers use derivatives as a risk management tool, primarily focusing on preserving the value of their underlying assets or liabilities rather than seeking speculative profits.
Speculators:
- Speculators are market participants who aim to profit from price movements in financial markets by taking on risk. They assume positions with the expectation of profiting from future price changes.
- For instance, a speculator may buy a futures contract on a commodity, such as oil, with the belief that the price will increase. If the price indeed rises, the speculator can sell the contract at a higher price and realize a profit.
- Speculators can be individuals, institutional investors, or hedge funds seeking to generate returns from market fluctuations.
Unlike hedgers, speculators do not have an underlying exposure or asset to protect. They actively take on risk in the hopes of earning profits from market movements.
Arbitrageurs:
- Arbitrageurs are market participants who take advantage of price discrepancies or inefficiencies in different markets or related securities. They aim to make risk-free profits by exploiting these pricing imbalances.
- Arbitrage opportunities can arise when the same asset or security trades at different prices in different markets or when related assets have price discrepancies.
- For example, an arbitrageur may simultaneously buy an asset at a lower price in one market and sell it at a higher price in another market, profiting from the price differential.
11. What is the relationship between futures price and spot price as the delivery period?
As the delivery period for a futures contract is approached, the futures price converges to the spot price of the underlying asset. When the delivery period is reached, the futures price equals—or is very close to—the spot price.
Relationship between futures price and spot price as the delivery period is approached:
(a) Futures price above spot price
We first suppose that the futures price is above the spot price during the delivery period. Traders then have a clear arbitrage opportunity:
1. Sell (i.e., short) a futures contract
2. Buy the asset
3. Make delivery.
These steps are certain to lead to a profit equal to the amount by which the futures price exceeds the spot price. As traders exploit this arbitrage opportunity, the futures price will fall.
b) Futures price below spot price
Suppose the futures price is below the spot price during the delivery period. Companies interested in acquiring the asset will find it attractive to enter into a long futures contract and then wait for delivery to be made. As they do so, the futures price will tend to rise. The result is that the futures price is very close to the spot price during the delivery period.
12. Can you explain the operation of margin account in the future contract?
If two traders get in touch with each other directly and agree to trade an asset in the future for a certain price, there are obvious risks. One of the traders may regret the deal and try to back out. Alternatively, the trader simply may not have the financial resources to honor the agreement. One of the key roles of the exchange is to organize trading so that contract defaults are avoided. This is where margin accounts come in.The operation of margin accounts involves several key components:
a) Initial Margin: This is the minimum amount of funds that must be deposited by the trader to open a futures position. The initial margin requirement is set by the exchange or broker and is typically a percentage of the total contract value. It serves as a form of security against potential losses.
b) Maintenance Margin: Once a futures position is open, the trader must maintain a certain level of funds in the margin account known as the maintenance margin. The maintenance margin is typically lower than the initial margin but is still required to be maintained to avoid a margin call. The maintenance margin is usually about 75% of the initial margin.
c) Margin Call: If the account value falls below the maintenance margin level due to adverse price movements, the broker will issue a margin call. A margin call requires the trader to deposit additional funds into the margin account to bring it back above the maintenance margin level. Failure to meet the margin call may result in the broker liquidating the position to cover the losses.
d) Variation Margin: If the balance in the margin account falls below the maintenance margin, the trader receives a margin call and is expected to top up the margin account to the initial margin level by the end of the next day. The extra funds deposited are known as a variation margin. If the trader does not provide the variation margin, the broker closes out the position.
Note: Margin requirements may depend on the objectives of the trader. A bona fide hedger, such as a company that produces the commodity on which the futures contract is written, is often subject to lower margin requirements than a speculator. The reason is that there is deemed to be less risk of default.
13. Does OTC market have any intermediatory who act as clearing house between 2 parties?
In an attempt to reduce credit risk, the OTC market has borrowed some ideas from exchange-traded markets. Central Counterparties (CCPs) are clearing houses for standard OTC transactions that perform much the same role as exchange clearing houses.
Central Counterparties (CCPs) play a crucial role in the over-the-counter (OTC) market by providing clearing and settlement services for OTC derivatives transactions. Their primary function is to act as a trusted intermediary between the buyer and seller, effectively becoming the buyer to every seller and the seller to every buyer. Here are the key roles of CCPs in the OTC market:
a) Risk Management: CCPs play a vital role in managing counterparty credit risk. When a trade is executed between two parties in the OTC market, the CCP becomes the central counterparty to both sides of the transaction. By assuming the counterparty risk, CCPs reduce the credit risk between market participants. They ensure that each party fulfills its obligations by collecting margin requirements, monitoring positions, and enforcing risk management measures.
b) Clearing and Settlement: CCPs provide clearing services by acting as an intermediary for the confirmation, matching, and reconciliation of OTC derivatives trades. They establish standardized procedures for trade validation, which streamline the settlement process. CCPs also facilitate the final settlement of trades by ensuring the timely transfer of funds and securities between the counterparties.
c) Margining and Collateral Management: CCPs impose margin requirements on market participants to cover potential losses. They collect initial margin and variation margin from both sides of the trade, which acts as collateral. By monitoring the value of the positions and adjusting margin requirements, CCPs help manage the risk associated with price fluctuations. Additionally, CCPs manage collateral efficiently, ensuring its availability and liquidity.
d) Default Management: In the event of a participant’s default, CCPs play a critical role in mitigating the systemic impact on the market. They have established default management procedures to handle such situations. CCPs may use various tools such as close-out netting, hedging strategies, and the use of default funds to manage the default and ensure the integrity and stability of the market.
14. Can you explain different types of orders placed by Traders in the future market?
In the futures market, traders can place various types of orders to execute their trades. Here are some common types of orders used in the futures market:
a) Market Order: A market order is an instruction to buy or sell a futures contract at the prevailing market price. The order is executed immediately at the best available price in the market. Market orders provide a guarantee of execution but do not guarantee a specific price.
b) Limit Order: A limit order is an instruction to buy or sell a futures contract at a specified price or better. For a buy limit order, the specified price must be below the current market price, while for a sell limit order, the specified price must be above the current market price. Limit orders provide control over the execution price but do not guarantee immediate execution.
c) Stop Order: A stop order becomes a market order when a specific price level, known as the stop price, is reached. For a buy stop order, the stop price is above the current market price, and for a sell stop order, the stop price is below the current market price. Stop orders are used to trigger trades once a certain price level is breached, often to enter or exit a position or to protect against potential losses.
d) Stop Limit Order: A stop limit order combines features of a stop order and a limit order. It becomes a limit order when the stop price is reached. The stop price activates the order, and the trader specifies a limit price that sets the maximum or minimum price at which they are willing to buy or sell. If the limit price is not reached, the order may not be filled.
e) Market on Close (MOC) Order: A market on close order is an instruction to buy or sell a futures contract at the market price during the closing auction period. MOC orders are executed as close to the market close as possible and are commonly used by traders who want to capture the closing price.
15. Differences in forward and future contract?
Forward contracts and futures contracts are both derivatives that involve an agreement to buy or sell an asset at a predetermined price and date in the future. However, there are several key differences between the two:
16. What is an option?
An option is a financial derivative contract that gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price (strike price) within a specified period (until expiration). It provides the buyer with the opportunity, but not the obligation, to take a certain action related to the underlying asset.
It should be emphasized that an option gives the holder the right to do something. The holder does not have to exercise this right. This is what distinguishes options from forwards and futures, where the holder is obligated to buy or sell the underlying asset. Whereas it costs nothing to enter into a forward or futures contract, except for margin requirements, there is a cost to acquiring an option.
PS: The actual expiration day is the third Friday of the expiration month.
17. What is a call option?
A call option gives the holder the right, but not the obligation, to buy an underlying asset at a predetermined price (strike price) within a specified period (until expiration). If the option is exercised, the buyer of the call option purchases the underlying asset from the option seller (writer) at the strike price.
Key aspects of call options
- Buyer/Holder: The person who purchases the call option, acquiring the right to buy the underlying asset.
- Seller/Writer: The person who sells or writes the call option, thereby granting the buyer the right to buy the underlying asset.
- Strike Price: The predetermined price at which the buyer has the right to purchase the underlying asset.
- Expiration Date: The date on which the option contract expires, after which the option is no longer valid.
- Premium: The price paid by the buyer to the seller for the call option.
Example: Profit from buying a European call option on one share of a stock.
- Option price = $5
- Strike price = $10
18. What is a put option?
A put option gives the holder the right, but not the obligation, to sell an underlying asset at a predetermined price (strike price) within a specified period (until expiration). If the option is exercised, the buyer of the put option sells the underlying asset to the option seller (writer) at the strike price.
Note: The price of a call option decreases as the strike price increases, while the price of a put option increases as the strike price increases. Both types of option tend to become more valuable as their time to maturity increases.
Example: Profit from buying a European put option on one share of a stock.
- Option price = $7
- Strike price = $70
Note: There are two sides to every option contract. On one side is the investor who has taken the long position (i.e., has bought the option). On the other side is the
investor who has taken a short position (i.e., has sold or written the option).
The writer of an option receives cash up front, but has potential liabilities later.
19. What is a payoff from Long Position in Call Option?
Payoffs from positions in European options: (a) long call
Payoff Equation: max (ST – k, 0)
20. What is a payoff from Short Position in Call Option?
Payoffs from positions in European options: (b) short call
Payoff Equation: min (K – ST, 0)
21. What is a payoff from Long Position in Put Option?
Payoffs from positions in European options: (c) long put;
Payoff Equation: max (K – ST, 0)
22. What is a payoff from Short Position in Put Option?
Payoffs from positions in European options: (d) short put
Payoff Equation: min (ST – K, 0)
23. Can you explain in the money, at the money and out of the money
of an Option?
Options are referred to as in the money, at the money, or out of the money.
If S is the stock price and K is the strike price,
A call option is:
- In the money when S > K,
- At the money when S = K, and
- Out of the money when S < K.
A put option is:
- In the money when S < K
- At the money when S = K, and
- Out of the money when S > K
24. What do you mean by bid offer spread?
A market maker for a certain option is an individual who, when asked to do so, will quote both a bid and an offer price on the option. The bid is the price at which the market maker is prepared to buy, and the offer or asked is the price at which the market maker is prepared to sell. At the time the bid and offer prices are quoted, the market maker does not know whether the trader who asked for the quotes wants to buy or sell the option. The offer is always higher than the bid, and the amount by which the offer exceeds the bid is referred to as the bid–offer spread.
25. What are different underlying assets in an option contract?
Options are derivative contracts that provide the right, but not the obligation, to buy or sell an underlying asset at a predetermined price (strike price) within a specified time period. The underlying asset can vary depending on the type of option contract. Here are some common types of underlying assets in options:
- Stocks: Stock options are among the most widely traded options. They have stocks of individual companies as their underlying assets. For example, options on shares of Apple Inc. would have the Apple stock as their underlying asset.
- Stock Indices: Options can be based on stock market indices, such as the S&P 500, Dow Jones Industrial Average, or NASDAQ-100. These options allow investors to gain exposure to a broad market index rather than individual stocks.
- Exchange-Traded Funds (ETFs): Options can also be based on ETFs, which are investment funds that trade on stock exchanges. ETF options provide investors with the ability to gain exposure to a diversified portfolio of assets represented by the underlying ETF.
- Currencies: Options on currencies, commonly known as foreign exchange options or forex options, have currency pairs as their underlying assets. For instance, an option could be based on the exchange rate between the U.S. dollar and the Euro (USD/EUR).
- Commodities: Options on commodities allow investors to trade on the price movements of various physical goods or raw materials. Examples of underlying commodities include gold, silver, crude oil, natural gas, agricultural products, and more.
- Interest Rates: Options can be based on interest rates, specifically interest rate futures contracts. These options allow market participants to hedge or speculate on changes in interest rates, such as those based on government bonds or short-term interest rate benchmarks.
- Bonds: Some options have bonds as their underlying assets. These options are less common compared to other types of options, but they exist and can be used for hedging or investment purposes.
26. What are the factors affecting price of the Options?
There are six factors affecting the price of a stock option:
- The current stock price, S0
- The strike price, K
- The time to expiration, T
- The volatility of the stock price, Sigma
- The risk-free interest rate, r
- The dividends that are expected to be paid
27. How do Traders use forward contracts for hedging? Give an example.
Suppose a US-based company is expecting to receive a payment of €1,000,000 from a customer in three months. However, the company is concerned about the potential depreciation of the euro against the US dollar during that period, which would result in a lower value of the payment in USD. To hedge against this risk, the company decides to enter into a forward contract with a bank.
The current exchange rate is 1 euro = 1.20 US dollars. The company wants to lock in the exchange rate to protect against a potential depreciation. They enter into a three-month forward contract to sell €1,000,000 at a predetermined exchange rate of 1 euro = 1.18 US dollars.
Here’s how the hedging process using forward contracts works:
1. Entering into the Forward Contract:
The company enters into a forward contract with the bank, agreeing to sell €1,000,000 at the rate of 1 euro = 1.18 US dollars in three months. By doing so, the company has effectively locked in the exchange rate, eliminating the risk of a potential depreciation of the euro.
2. Payment from the Customer:
Three months later, the company receives the payment of €1,000,000 from the customer. At this point, the exchange rate may have changed, but the company is protected by the forward contract.
3. Settling the Forward Contract:
Since the forward contract has reached its expiration, the company settles the contract with the bank. If the exchange rate at expiration is 1 euro = 1.15 US dollars, the company will sell €1,000,000 at the predetermined rate of 1 euro = 1.18 US dollars. As a result, the company will receive $1,180,000 (€1,000,000 x 1.18) from the bank.
4. Calculating the Hedging Outcome:
The company compares the amount received from the bank ($1,180,000) with the current market exchange rate (1 euro = 1.15 US dollars). Without the hedge, the company would have received $1,150,000 (€1,000,000 x 1.15) at the current exchange rate. The difference of $30,000 represents the protection provided by the forward contract.
By using the forward contract, the company has successfully hedged its exposure to currency exchange rate risk. Regardless of the actual exchange rate at the time of payment, the company is guaranteed to receive the predetermined amount in US dollars, thus mitigating the risk of currency fluctuations.
It’s important to note that while forward contracts can provide effective hedging, they also come with certain risks and limitations, such as potential opportunity costs if the exchange rate moves favorably for the hedger. Careful consideration of the company’s specific circumstances and risk management goals is essential when implementing a hedging strategy using forward contracts.
28. Explain put call parity?
Put-call parity shows the relationship that has to exist between European put and call options that have the same underlying asset, expiration, and strike prices. This concept says the price of a call option implies a certain fair price for the corresponding put option with the same strike price and expiration and vice versa.
Put-call parity doesn’t apply to American options because you can exercise them before the expiry date. If the put-call parity is violated, then arbitrage opportunities arise.
Consider the following two portfolios:
Portfolio A: One European call option plus a zero-coupon bond that provides a payoff of K at time T
Portfolio C: One European put option plus one share of the stock
If ST > K, both portfolios are worth ST at time T; if ST < K, both portfolios are worth K at time T. In other words, both are worth max (ST, K)
The components of portfolio A are worth c and Ke^(-rT) today, and the components of portfolio C are worth p and S0 today. Hence,
This relationship is known as put–call parity. It shows that the value of a European call with a certain exercise price and exercise date can be deduced from the value of a European put with the same exercise price and exercise date, and vice versa.
For a dividend-paying stock, the put–call parity relationship is
29. Why it is never optimal to exercise an American call option on a
non-dividend-paying stock before the expiration date.
It is generally not optimal to exercise an American call
option on a non-dividend-paying stock before the expiration date because
Time Value of the Option: An
option’s price consists of two components: intrinsic value and time value. The
intrinsic value is the difference between the stock price and the strike price,
and for time value means, you would rather delay paying the strike price by
exercising it as late as possible. You could use that money to earn interest.
So, a positive intrinsic value plus time value implies that you are better off
selling the option rather than exercising it early. This is true for a
non-dividend paying stock.
Opportunity Cost: By
exercising an option early, the option holder loses the opportunity to benefit
from any potential future price movements in the underlying stock. If the stock
price continues to rise, holding the option rather than exercising it early
allows the holder to capture additional profit.
Risk of Price Reversal:
If the stock price declines after exercising an American call option, the
option holder would have been better off not exercising early. By holding the
option, the holder maintains the right to participate in any potential price
increases, while limiting the loss to the premium paid for the option.
30. When is it optimal to exercise an American call option?
Here are some situations when it may be optimal to exercise an American option:
1. Close to Expiration: As the expiration date approaches, the time value of the option diminishes, and the intrinsic value becomes the dominant factor. If an American option is deep in-the-money and close to expiration, it may be beneficial to exercise to capture the intrinsic value rather than holding the option and risking any adverse price movements.
2. Dividend Payments: For stocks that pay dividends, it may be advantageous to exercise an American call option just before the ex-dividend date. By exercising the option, the holder can acquire the shares and be eligible to receive the upcoming dividend payment.
3. Market Events or News: Significant market events or company-specific news can impact the value of the underlying asset. If the option holder believes that the stock price will experience a substantial move due to such events, exercising the option to take a position in the stock can be favorable.
4. Risk Management: If the option holder wants to limit their risk exposure or lock in profits, they may choose to exercise an American option. By exercising, they can realize the gains and eliminate any further market risk associated with holding the option.
31. How do Traders use Option contracts for hedging? Give an example.
Options can also be used for hedging.
Consider an investor who in May of a particular year owns 1,000 shares of a particular company. The share price is $28 per share. The investor is concerned about a possible share price decline in the next 2 months and wants protection.
The investor could buy 10 July put option contracts on the company’s stock with a strike price of $27.50. Each contract is on 100 shares, so this would give the investor the right to sell a total of 1,000 (10*100) shares for a price of $27.50.
If the quoted option price is $1, then each option contract would cost 100 X 1 = $100 and the total cost of the hedging strategy would be 10 X 100 = $1,000. The strategy costs $1,000 but guarantees that the shares can be sold for at least $27.50 per share during the life of the option. If the market price of the stock falls below $27.50, the options will be exercised, so that $27,500 is realized for the entire holding. When the cost of the options is taken into account, the amount realized is $26,500. If the market price stays above $27.50, the options are not exercised and expire worthless. However, in this case the value of the holding is always above $27,500 (or above $26,500 when the cost of the options is taken into account).
32. Difference between futures and options?
Futures and options are both derivative contracts used in financial markets, but they have some key differences in terms of their structure, obligations, and potential outcomes. Here are the main differences between futures and options:
a) Obligations:
Futures: In a futures contract, both the buyer (long position) and the seller (short position) are obligated to fulfill the contract’s terms. This means that at the contract’s expiration, the buyer must buy the underlying asset, and the seller must sell the asset at the predetermined price.
Options: In an options contract, the buyer has the right, but not the obligation, to exercise the contract. The buyer can choose whether to buy or sell the underlying asset at the predetermined price (strike price) within the specified period (until expiration). The seller, on the other hand, is obligated to fulfill the buyer’s decision if the buyer exercises the option.
b) Risk/Reward Profile:
Futures: Both buyers and sellers of futures contracts are exposed to unlimited risk and unlimited profit potential. Profits or losses are directly tied to the price movement of the underlying asset.
Options: The risk and reward profile of options differs for buyers and sellers. Options buyers have limited risk, as their potential loss is limited to the premium paid for the option. However, their profit potential is unlimited. Option sellers, on the other hand, have limited profit potential (the premium received) but face potentially unlimited risk if the option is exercised.
c) Usage:
Futures: Futures contracts are more commonly used in certain markets, such as commodities, currencies, and interest rates. They are often favored by institutions and professional traders for hedging, speculation, and risk management.
Options: Options contracts are widely used across various markets, including stocks, commodities, currencies, and indices. They are popular among traders and investors for various strategies, including hedging, speculation, income generation, and risk management.
Futures and options are similar instruments for speculators in that they both provide a way in which a type of leverage can be obtained. However, there is an important difference between the two. When a speculator uses futures, the potential loss as well as the potential gain is very large. When options are used, no matter how bad things get, the speculator’s loss is limited to the amount paid for the options.
33. Explain carefully the difference between selling a call option and buying a put option?
Selling a call option and buying a put option are both strategies used in options trading, but they have opposite perspectives and payoff structures. Here’s a careful explanation of the difference between the two:
Selling a Call Option:
When you sell a call option, you are known as the “option writer” or “seller.” By selling a call option, you are giving someone else the right to buy the underlying asset from you at a predetermined price (strike price) within a specific period (until expiration). In this case, you are obligated to sell the asset if the option buyer exercises their right.
Key Points:
- As the seller, you receive a premium from the buyer upfront for selling the call option.
- You have the obligation to sell the underlying asset at the strike price if the option is exercised.
- Your maximum profit is limited to the premium received, and your potential losses can be unlimited if the underlying asset’s price rises significantly.
Buying a Put Option:
When you buy a put option, you are known as the “option holder” or “buyer.” By buying a put option, you acquire the right, but not the obligation, to sell the underlying asset at a predetermined price (strike price) within a specific period (until expiration). This strategy is typically employed when you anticipate a potential decline in the price of the underlying asset.
Key Points:
- As the buyer, you pay a premium to the option seller for acquiring the put option.
- You have the right to sell the underlying asset at the strike price, but you are not obligated to do so.
- Your maximum potential loss is limited to the premium paid, while your potential profit increases as the price of the underlying asset decreases.
34. What is forward rate agreement?
A forward rate agreement (FRA) is an over-the-counter contract designed to fix the interest rate that will apply to either borrowing or lending a certain principal amount during a specified future time period.
Most FRAs are based on LIBOR/SOFR. A trader who will borrow a certain principal amount at SOFR for a future period can enter into an FRA where for the specified time period SOFR will be received on the principal amount and a predetermined fixed rate will be paid on the principal amount. This converts the uncertain floating SOFR rate to a fixed rate. If SOFR proves to be greater (less) than the fixed rate the payoff from the FRA is positive (negative).
Key Points
- Trader pays fixed rate and receive floating (SOFR).
- If SOFR > fixed = Positive Cashflow to Trader; because he needs to pay lower fixed rate even though SOFR (floating rate) is high
- If SOFR < fixed = Negative Cashflow to Trader; because he still needs to pay higher fixed rate even though SOFR is low.
35. Define Macaulay Duration of a Bond?
The duration of a bond, as its name implies, is a measure of how long the holder of the bond has to wait before receiving the present value of the cash payments. A zero-coupon bond that lasts n years has a duration of n years. However, a coupon-bearing bond lasting n years has a duration of less than n years, because the holder receives some of the cash payments prior to year n.
Mathematically, Macaulay duration is calculated as the sum of the present value of each cash flow multiplied by the time until its receipt, divided by the bond’s current market price. It is expressed in terms of years.
The duration of the bond, D, is defined as
Q36. Consider a 3-year 10% coupon bond with a face value of $100. Suppose that the yield on the bond is 12% per annum with continuous compounding.
- This means that y = 0.12.
- Coupon payments of $5 are made every 6 months.
- The present values of the bond’s cash flows, using the yield as the discount rate, are shown in column 3 (e.g., the present value of the first cash flow is 5e^(-0.12*0.5) = 4.709
- The weights are calculated by: 4.709/94.213 = 0.050
- Adding all the Time X Weight gives Duration
Therefore, Duration is 2.653 years
Q37. Define Modified Duration of a Bond?
Modified duration is a measure used in fixed-income investments to estimate the sensitivity of a bond’s price to changes in interest rates. It is a key tool for assessing interest rate risk and understanding the potential impact of interest rate movements on bond prices.
Modified duration is a modified version of Macaulay duration, adjusted to provide a percentage change in the bond’s price for a given change in interest rates. Unlike Macaulay duration, which is expressed in years, modified duration is expressed as a decimal or percentage.
The formula to calculate modified duration is as follows:
Note: DV01 is the price change from a 1-basis-point increase in all rates. Gamma is the change in DV01 from a 1-basis-point increase in all rates.
Q38. What are some relationships between duration and bond?
- The lower the coupon, the higher the duration.
- The higher the coupon, the lower the duration.
- The longer the term to maturity, the higher the duration.
- The shorter the term to maturity, the lower the duration.
- The smaller the duration, the smaller the price volatility of the bond.
- The greater the duration, the greater the price volatility of the bond.
Q39. How to calculate the duration of a Portfolio?
To calculate the duration of a portfolio, you need to consider the individual bond holdings within the portfolio and their respective weights or proportions. The process involves calculating the weighted average duration of the bonds based on their weights in the portfolio. Here are the steps:
- Determine the weight of each bond in the portfolio: Identify the proportion or weight of each bond’s market value relative to the total market value of the portfolio. For example, if a portfolio consists of three bonds with weights of 40%, 30%, and 30%, respectively, the total weights should add up to 100%.
- Calculate the duration of each bond: Calculate the duration of each individual bond using the Macaulay duration formula. This involves determining the present value of each bond’s cash flows, weighted by their respective times to receipt, and dividing it by the bond’s current market price.
- Calculate the weighted average duration: Multiply the duration of each bond by its corresponding weight, and then sum up the weighted durations for all the bonds in the portfolio. This gives you the weighted average duration of the portfolio.
Mathematically, the formula to calculate the duration of a portfolio is:
Portfolio Duration = (Weight1 × Duration1) + (Weight2 × Duration2) + … + (WeightN × DurationN);
where Weight1, Weight2, …, WeightN are the weights of the individual bonds, and Duration1, Duration2, …, DurationN are their respective durations.
Q40. What are the limitations of duration?
While duration is a widely used measure for assessing interest rate risk in fixed-income investments, it has some limitations that should be considered:
Assumption of a Linear Relationship: Duration assumes a linear relationship between bond prices and interest rates. It assumes that the bond’s price will change proportionally with a change in interest rates. In reality, bond price-yield relationships may not be perfectly linear, especially for bonds with embedded options or bonds with non-parallel shifts in the yield curve.
Non-Parallel Shifts: Duration assumes that there is a parallel shift in yield between different maturities of a bond. In reality, yield curves can shift in a non-parallel manner. Different maturities of bonds may experience different changes in yields. For example, a steepening or flattening of the yield curve implies that short-term and long-term interest rates change by different magnitudes. Duration alone cannot capture the impact of non-parallel shifts accurately.
Sensitivity Limited to Small Interest Rate Changes: Duration provides a good estimate of a bond’s price sensitivity to small changes in interest rates. However, its accuracy diminishes as interest rate changes become more significant. Large interest rate changes can lead to convexity effects, which impact bond prices differently than what duration predicts.
Ignores Credit Risk and Other Factors: Duration primarily focuses on interest rate risk and assumes all other factors remain constant. It does not account for credit risk, liquidity risk, issuer-specific events, or other market factors that can impact bond prices. Duration is not a comprehensive measure of overall risk in a bond or a portfolio.
Time Horizon Mismatch: Duration assumes a constant cash flow profile for the bond until maturity. However, in reality, bond cash flows can be impacted by factors such as call provisions, prepayments, or changes in coupon rates. Duration may not accurately capture the price sensitivity when these factors come into play.
Different Durations for Different Bonds: A portfolio’s overall duration is a weighted average of the individual bond durations. However, bonds within a portfolio may have different durations, and the impact of interest rate changes may not be uniform across all bonds.
Q41. Define Key Rate Duration? How is it better than Duration?
Key rate duration, also known as partial duration or partial key rate duration, is a risk measure used in fixed-income investments to analyze the sensitivity of a bond’s price to changes in specific key interest rates along the yield curve. It provides insights into how a bond’s price will react to changes in specific segments of the yield curve, rather than assuming a parallel shift across all maturities.
Key rate duration allows investors to assess the interest rate risk associated with specific segments of the yield curve and provides a more granular view compared to overall duration. It helps in identifying which maturity points or segments of the yield curve contribute most to the bond’s price sensitivity and risk exposure. This information can be valuable for portfolio managers, enabling them to make informed decisions about portfolio positioning and risk management based on the specific interest rate scenarios they anticipate.
Q42. Define Convexity of a Bond?
Convexity is the second derivative of the price-yield function with respect to yield. It measures the rate of change of the instrument’s duration as yields change. By considering the curvature of the price-yield relationship, convexity accounts for the non-linear relationship between price and yield.
Q43. What is positive convexity and negative convexity of a bond?
Convexity can have either a positive or negative value. Positive convexity implies that the instrument’s price increases at an increasing rate as yields decrease and decreases at a decreasing rate as yields increase. This means that the instrument exhibits a greater price increase than what duration alone predicts when yields decrease and a smaller price decrease than what duration predicts when yields increase. Most traditional bonds exhibit positive convexity.
Negative convexity implies that as interest rates decrease, the price of the instrument rises at a decreasing rate compared to what would be expected based on duration alone. Conversely, as interest rates increase, the price declines at an increasing rate relative to the predictions of duration. Negative convexity refers to a characteristic of certain financial instruments, typically bonds with embedded options, where the price-yield relationship deviates from the typical positive convexity observed in traditional bonds.
Convexity is typically expressed as a decimal or percentage. A higher convexity value indicates a greater sensitivity of the instrument’s price to changes in yield.
Q43. What is Interest Rate Futures?
Interest rate futures provide a way for market participants to lock in or speculate on future interest rates. For example, a trader who believes that interest rates will rise in the future can enter into a futures contract to buy the underlying interest rate at a specific price (known as the futures price) and profit if rates actually increase. On the other hand, a market participant who wants to protect against potential interest rate declines can sell interest rate futures and profit if rates actually fall.
Interest rate futures are financial derivatives contracts that are based on the future value of an underlying interest rate. These futures contracts enable market participants to speculate on or hedge against changes in interest rates. They are commonly used by financial institutions, corporations, and individual traders to manage their exposure to interest rate movements.
The underlying interest rate in interest rate futures can be based on various reference rates, such as government bond yields, interbank lending rates (such as LIBOR), SOFR, or other benchmark interest rates. The futures contract specifies the agreed-upon interest rate, the notional principal amount, and the maturity date.
Q44. What is common Interest Rate Future contracts traded in the financial markets?
The CME Group offers a variety of interest rate futures contracts that allow market participants to manage and trade interest rate risk. Here are a few examples of interest rate futures contracts offered by the CME Group:
- Eurodollar Futures
- S. Treasury Futures
- One-month SOFR
- Three-month SOFR
- 30 days federal fund future
Link: https://www.cmegroup.com/markets/interest-rates.html#overview
Q45. What is Eurodollar Future?
Eurodollar futures are financial derivatives contracts that allow market participants to speculate on or hedge against changes in short-term U.S. dollar interest rates. These futures contracts are traded on the Chicago Mercantile Exchange (CME) and are based on the interest rates of U.S. dollar-denominated deposits held outside the United States, commonly referred to as Eurodollars.
Here are the key elements of Eurodollar futures:
- Underlying Asset: The underlying asset of Eurodollar futures is a notional principal value of a three-month U.S. dollar-denominated deposit held in offshore banks. These deposits represent U.S. dollars held outside the jurisdiction of the United States.
- Contract Size: Each Eurodollar futures contract represents a notional value of $1 million. The contract size is used to calculate the dollar value of the futures contract.
- Maturity: Eurodollar futures have specific expiration months, following the standard futures expiration cycle. The most actively traded contracts typically have maturities up to 10 years.
- Price Quotation: The prices of Eurodollar futures contracts are quoted as 100 minus the annualized interest rate. For example, a quoted price of 98.50 implies an annualized interest rate of 1.50%.
- Settlement: Eurodollar futures contracts are settled in cash. There is no physical delivery of the underlying deposits. Upon contract expiration, the settlement price is determined by the average of the daily settlement prices over a specified period, usually the last three trading days.
- Margin Requirements: Market participants who trade Eurodollar futures are required to deposit an initial margin with their broker. The margin represents a fraction of the contract’s value and serves as collateral against potential losses.
The contract is quoted on an index price basis. For example, the index price might be 94.52. From the futures index price, the annualized futures three-month LIBOR is determined as follows: 100 minus the index price. For example, a Eurodollar futures index price of 94.52 means the parties to this contract agree to buy or sell three-month LIBOR for 5.48%. Since the underlying is an interest rate that obviously cannot be delivered, this contract is a cash settlement contract.
Q47. What is Treasury Bond Future?
Treasury bond futures are financial derivatives that allow market participants to speculate on or hedge against changes in the future price of U.S. Treasury bonds. These futures contracts are traded on exchanges and represent an agreement to buy or sell Treasury bonds at a specified price and date in the future.
- Underlying Asset: Treasury bond futures contracts are based on specific Treasury bonds, typically benchmark bonds with longer maturities, such as the 10-year or 30-year Treasury bonds.
- Contract Specifications: Treasury bond futures have standardized contract specifications that include the delivery date, contract size (representing the face value of the underlying bonds), the conversion factor (to determine the bond’s deliverable value), and the quoted price convention.
- Pricing and Quoting: Treasury bond futures are quoted as prices, which represent a percentage of the face value of the underlying bond. For example, a price quote of 99.50 indicates 99.50% of the face value. The price movement is typically in 1/32 increments, with each 1/32 representing a price change of $31.25 per contract.
- Delivery Options: While cash settlement is the typical outcome, some Treasury bond futures contracts offer the option for physical delivery of the underlying Treasury bonds. However, physical delivery is less common and primarily used by participants engaged in arbitrage strategies or those with specific delivery requirements.
- Risk Management and Hedging: Treasury bond futures provide a means for market participants to manage interest rate risk. Investors and traders can take long (buy) or short (sell) positions in Treasury bond futures to hedge their exposure to changes in bond prices or interest rates.
- Contract Expiration: Treasury bond futures contracts have specific expiration dates, usually falling in quarterly cycles (e.g., March, June, September, December). As the contract approaches expiration, traders can either roll their positions into a new contract or close out their positions.
The price of bond futures can be calculated on the expiry date as:
Price = (Most recent settlement price x Conversion Factor) + Accrued Interest
Q47. What is Cheapest to Deliver Bond?
At any given time during the delivery month, there are many bonds that can be delivered in the Treasury bond futures contract. These vary widely as far as coupon and maturity are concerned. The party with the short position can choose which of the available bonds is ‘‘cheapest’’ to deliver. Because the party with the short position receives
Cheapest-to-deliver bond formula:
Quoted bond price – (Most recent settlement price X Conversion factor)
Example: The party with the short position has decided to deliver and is trying to choose between the three bonds in the table below. Assume the most recent settlement price is 93-08, or 93.25.
The cost of delivering each of the bonds is as follows:
Bond 1: 99:50 – (93.25 X 1:0382) = $2.69
Bond 2: 143:50 – (93.25 X 1:5188) = $1.87
Bond 3: 119:75 – (93.25 X 1:2615) = $2.12
The cheapest-to-deliver bond is Bond 2
Q48. What are different day count conventions used for calculating
interest rates?
Day count conventions are methods used to calculate the actual number of days between two dates for interest rate calculations. Different financial instruments and markets may use different day count conventions, and the choice of convention can impact the calculation of interest payments or accrued interest.
Day Count Formula:
Here are a few common day count conventions used in interest rate calculations:
a) Actual/Actual (A/A): This convention calculates the actual number of days in the calculation period and divides it by the actual number of days in the year. It is considered one of the most accurate day count conventions because it takes into account leap years. For example, if the calculation period is from January 1 to June 30, and there are 183 days in that period and 365 days in the year, the day count fraction would be 183/365.
b) Actual/360 (A/360): This convention assumes a year of 360 days, regardless of leap years. The actual number of days between two dates is divided by 360 to calculate the day count fraction. For example, if the calculation period is from January 1 to June 30, and there are 181 days in that period, the day count fraction would be 181/360.
c) Actual/365 (A/365): Similar to Actual/360, this convention assumes a year of 365 days, regardless of leap years. The actual number of days between two dates is divided by 365 to calculate the day count fraction.
d) 30/360 (30/360): This convention assumes a year of 360 days and divides the actual number of days between two dates by 360. However, it simplifies the calculations by assuming that each month has 30 days. For example, if the calculation period is from January 1 to June 30, the convention would consider 5 months (January to May) as having 30 days each and June as having 30 days. Therefore, the day count fraction would be 180/360.
Q49. Define Swaps?
Swaps are financial derivatives that involve the exchange of cash flows or financial instruments between two parties over a specified period of time. Swaps allow parties to customize their exposure to various factors, such as interest rates, currencies, commodities, or credit.
Q50. What are different kinds of swaps available in the financial market?
There are several different types of swaps, each designed to address specific risk exposures or financial needs. Here are some of the most common types of swaps:
1. Interest Rate Swaps (IRS): Interest rate swaps are the most prevalent type of swap. They involve the exchange of fixed-rate and floating-rate cash flows based on a notional principal amount. The fixed-rate payer pays a predetermined fixed interest rate, while the floating-rate payer pays a variable interest rate based on a reference rate such as LIBOR or a government bond yield.
2. Currency Swaps: Currency swaps involve the exchange of principal and interest payments denominated in different currencies. They are commonly used by companies with international operations to hedge foreign exchange risk or obtain financing in a different currency.
3. Commodity Swaps: Commodity swaps allow market participants to manage price risk associated with commodities. In a commodity swap, one party pays a fixed price for a specific quantity of a commodity, while the other party pays the prevailing market price. The commodity involved can be oil, natural gas, agricultural products, or any other tradable commodity.
4. Equity Swaps: Equity swaps involve the exchange of cash flows based on the performance of underlying stocks or equity indices. One party may pay the total return (dividends plus capital appreciation) on a specific stock or index, while the other party pays a fixed or floating rate.
5. Credit Default Swaps (CDS): Credit default swaps are used to hedge or speculate on credit risk. In a CDS, one party makes periodic premium payments to protect against the default of a specific reference entity (such as a corporation or government). If a credit event occurs, the protection buyer receives a payment from the protection seller.
These are just a few examples of the various types of swaps available in the financial markets. Each type of swap serves a specific purpose and allows market participants to manage or hedge different types of risks, adjust cash flow profiles, or gain exposure to specific assets or markets. It’s important to note that swaps can be highly complex, and professional advice and expertise are often sought when entering into swap transactions.