Financial Derivatives PDF

# Financial Derivatives ## Unit-3 ## Fundamental of Options Contract ### Notes ### What is an Options Contract - An options contract conveys the right to buy or sell a specified asset at a fixed price for a fixed length of time. - The important thing in an options contract is that the purchaser of t...

# Financial Derivatives ## Unit-3 ## Fundamental of Options Contract ### Notes ### What is an Options Contract - An options contract conveys the right to buy or sell a specified asset at a fixed price for a fixed length of time. - The important thing in an options contract is that the purchaser of the options contract has the right, but not an obligation, to sell or buy the asset. - This distinction separates an options contract from other derivatives contracts such as futures and forward contracts. - In the case of futures and forward contracts, the holder of the contract has an obligation to fulfill the terms of the contract, while the holder of an options contract is not legally obliged to take any further action. - Thus, the holder of an options contract may wish to fulfil their contractual right to buy or sell the asset only if it is economically advantageous to do so. - On the other hand, the holders of forward and futures contracts will have to fulfil their obligations even if it is disadvantageous to them. ### Options Terminologies #### The Underlying Asset - An options contract provides the buyer of an option with the right to buy or sell a specified asset. The asset on which the option is written is known as the underlying security or asset. #### Call and Put Options - In the options markets, there are two types of options, depending on whether the purchaser of the option has the right to buy or sell the underlying asset; these are called call options and put options. - A call option gives the purchaser of the option the right to buy the underlying asset at a fixed price at a future time. - A put option gives the purchaser of the option the right to sell the underlying asset at a fixed price at a future time. #### The Option Premium - The price that the buyer of the option pays the seller of the option is known as the option price or option premium. #### Buyers and Writers of Options - The person who purchases the option (whether it is a call option or a put option) is called an option buyer and they are said to hold the option long. - The person who sells the option (whether it is a call option or a put option) is called an option writer and they are said to have sold the option short. - The distinction between the option writer and buyer is important, because the right to exercise rests only with the option buyer. The option writer has the obligation to fulfil the terms of the contract in case the option buyer exercises their right under the options. ### Exercising Options - In the case of a call option, the option holder has the right to buy the underlying asset at a fixed price and they will buy the underlying asset using the options contract only if it is economically advantageous to do so. When an option holder decides to buy the underlying asset under the options contract, they are said to exercise the call option. - If the option holder finds that exercising the option will be economically disadvantageous, they will not exercise the option. - In a put option, the option holder has the right to sell the asset at a fixed price, and they will sell the asset under the options contract only if it is economically advantageous to do so. When an option holder decides to sell the property under the options contract, they will exercise the put option. - If the option holder finds that exercising the option will be economically disadvantageous, they will not exercise the option and it will expire without exercise. #### The Contract Size - The options contract also needs to specify the number of units of the underlying asset that can be bought or sold using the option. This is known as the contract size or market lot size. #### The Exercise Price or the Strike Price - All options contracts provide the price at which the asset will be bought or sold if the option is exercised. - This price is fixed and the seller of the option will have to either sell the asset at this fixed price to the holder of the option (in a call option) or buy the asset at this fixed price from the holder of the option (in a put option). This fixed price at which the asset will be traded under the options contract is known as the exercise price or strike price of the option. #### The Exercise Date or the Strike Date - All options contracts have a fixed maturity. That is, the option holders will have to make a decision as to whether they are going to exercise the option and either buy the underlying asset at the exercise price (if it is a call option) or sell the underlying asset at the exercise price (if a put option), by this fixed maturity date. The fixed maturity date of an options contract is known as the exercise date or strike date. ### American and European Options - Options contracts are classified as either American options or European options, depending on when the holders of the options contracts can exercise their right to buy or sell the asset during the maturity of the option. - If the options contract stipulates that the holder can exercise the right to buy or sell the asset at the fixed exercise price only on the fixed maturity date or exercise date, the option is referred to as a European option. - If the options contract stipulates that the holder can exercise the right to buy or sell the asset at the fixed exercise price at any time from the time of purchasing the option until and including the fixed maturity date or exercise date, the option is referred to as an American option. #### In-the-money, At-the-money and Out-of-money Options - Whenever the price of the underlying asset is such that exercising the option will provide a gain, the option is said to be in-the-money. - If exercise is likely to result in a loss, the option is said to be out-of-money. - If the price of the underlying asset is very close to the exercise price, the option is said to be at-the-money. | Type | Call | Put | |---|---|---| | At the Money | Strike = Spot | Strike = Spot | | In the Money | Strike < Spot | Strike > Spot | | Out of the Money | Strike > Spot | Strike < Spot | ### Options Trading - Options are traded on organised exchanges or on OTC markets. In OTC trading, the options brokers and dealers bring together buyers and writers and arrange the contract terms. - The volume of transactions in the OTC market is comparatively low and commission expenses are high. - There is transparency in exchange-traded contracts, as all the details of the trades are posted by the exchange and hence it is easy to regulate the activity in exchanges. On the other hand, OTC transactions are not transparent and it is very difficult to regulate the activity in OTC markets. - There is no standardization of options contracts and, therefore, OTC options are not generally tradable. Hence, the OTC market is suitable only for individuals and financial institutions that are looking for a particular contract to suit their purpose. - The major disadvantage of OTC options is the existence of counterparty risk. ### Options Trading - Margin Requirements - Options trading on exchanges also require that the writer of the options put up a margin, similar to the margin in futures trading. - The margin amount is usually calculated on the basis of the variability in stock price movements. Similar to futures trading, there will be initial margin requirements as well as a variation margin. - The margin account will be marked-to-market every day, and in case the margin amount goes below the variation margin requirement, the writer of the option will get a margin call. On receipt of a margin call, the writer of the option will have to provide additional cash to reach the initial margin amount, or the broker has the right to offset the contract. Similar to futures trading, the margin amount can be in cash or securities that are allowed by the exchange clearinghouse. - The margin needs to be posted only by the writer of the option, and not by the buyer. - This is different from futures trading, where both the buyers and the sellers of futures need to post margin. In the case of futures, both the buyers and the sellers of futures have obligations to fulfil at the time of maturity of the contract and, therefore, both need to post the margin. - However, in the case of options, only the writer of the option has obligations and the buyer gets the right to exercise. - Since options buyers do not have an obligation to fulfil their contract unless they exercise the option, they do not need to post any margin. ### Standardization of Contract - The success of options contracts in organized exchanges depends on how well the options are standardized. - Standardization requires that all parties know exactly what they are contracting for, and the exchange should clearly specify the following: - The option type: call or put option - The name of the underlying security - The contract size, that is, the number of underlying shares in the case of a stock option and the multiplier in the case of index options - The exercise date or strike date - The exercise price or strike price - The rule for exercise: European or American ### Price Quotes - **Symbol:** This is the symbol under which the option is traded on the NSE. - **Expiry Date:** This is the expiry date of the option. For Nifty index options, the expiry dates are in September 2009, October 2009, November 2009, December 2009, March 2010, June 2010, December 2010, June 2011, December 2011, June 2012, and December 2012. For Bharti Airtel options, the expiry dates are in September 2009, October 2009, and November 2009. - **Strike Price:** Both calls and puts are available for various strike prices for each expiry date. Table 11.3 shows the quotes only for a few of the exercise prices. - **Option Type:** This shows whether the option is a call or a put as well as whether it is American or European. CE refers to a European call, PE refers to a European put, CA refers to an American call, and PA refers to an American put. All index options are European options, and all stock options are American options. - **Open, High, Low, Close, and Settle:** These are the data regarding the option premium, which is determined in the exchange. They refer to the details of the opening price, highest price during the day, lowest price during the day, closing price of the day, and settlement price of the contract on that day. The settlement price is calculated by the exchange by taking the average of the prices during the last 30 minutes if there is trading in the options, and if there is no trading, the settlement price is calculated using a theoretical model. - **Contracts:** This shows the number of contracts that were traded that day. - **Value (in lakh):** This shows the total value of all contracts traded during the day. - **Open Interest:** This shows the number of outstanding contracts that require settlement on the expiry date. - **Change in Open Interest:** This shows the number of new contracts initiated that day. ### Types of Orders - Many types of orders can be placed by an investor while directing their broker to trade in options. The simplest type of order is a market order. A market order means that a trade must be carried out at the best prevailing market price, whatever that may be. 1. **A limit order** specifies a particular price. The order can be executed only at this price or at a price that is favorable to the buyer. For example, if the limit price is INR 15 for buying a call option on Allahabad Bank stock, the order can be executed and the call bought only for a price of INR 15 or less. Of course, there is no guarantee that this order will be executed at all, since the limit price may never be reached. 2. **A stop order** also specifies a particular price, and the order becomes a market order as soon as the stop price is reached. For example, if the stop price is INR 15 for the Allahabad Bank call, the order will become a market order as soon as the call price reaches INR 15. Since it is a market order, it will be executed at the best available price at that time. If the best price is INR 15.50, then the order will be executed at INR 15.50. The purpose of the stop order is generally to close out a position if unfavourable price movements take place, thereby limiting the amount of loss that is incurred. 3. **A stop-limit order** is a combination of a stop order and a limit order. The order becomes a limit order as soon as there is a bid or offer at a price equal to or less than the stop order price. Two prices must be specified in a stop-limit order: the stop price and the limit price. For example, an investor may place a stop-limit order with a stop price of INR 15 and a limit price of INR 15.30. When the market price reaches INR 15, the order becomes a limit order with a limit price of INR 15.30. - The orders can also specify time limits. Generally, an order is a day order, unless otherwise stated, and expires at the end of the day. A time-of-day order specifies a particular period of time during the day at which the order can be executed. An open order or a good-till-cancelled order is in effect until executed or until the end of trading in that contract. A fill-or-kill order must be executed immediately when received, or not at all. ### Offsetting Orders - An investor who has purchased an option can close out their position by issuing an offsetting order to sell the same option for same quantity. - Similarly, a person who has written an option can close out their position by issuing an offsetting order to purchase the same option for same quantity. ### What is a Call Option - A call option provides the right to buy the underlying security at a fixed price, known as the exercise price, at a specified future time, known as the exercise date. - Call options can be of either the American type or the European type. - An American call option can be defined as the right to buy the underlying asset at the exercise price on or before the exercise date. - CA Represents American Style Options - A European call option can be defined as the right to buy the underlying asset at the exercise price on the exercise date only. - CE Represents European Style Options - In India, NSE and BSE allow trading in European Style Options only. ### The Terminal Value of a Call Option - The value of a call option on the exercise date is known as its terminal value. - Consider a European option on the date of maturity. Since it is a European option, it can be exercised only on the exercise date, and in order to decide whether the buyer should exercise or not, it is important for them to know the value of the call option at that time. - Thus, the terminal value of a call option is important from that point of view. ### Exercising the Call Option (CE) - It is not profitable to exercise the Call option if the share price on expiry date is less than the exercise price. - If the share price on expiry date is higher than the exercise price, it is advisable to exercise the Call option. - **Only Buyers of Call Option can Exercise the Call Option.** - If the Share price and the exercise price on the terminal date or expiry date. - **Case 1:** If the exercise price (SX) > terminal stock price (ST), do not exercise; the value of the call option is zero. - **Case 2:** If the exercise price (SX) < terminal stock price (ST), exercise; the value of the call option is (ST - SX). $Terminal\ value\ =\ (S_T - S_X)\ if\ S_T > S_X$ $Terminal\ value\ =\ 0\ if\ S_T < S_X$ This can be shortened to: $Terminal\ value\ of\ a\ call\ =\ Max\ (S_T - S_X, 0)$ ### Gains or Loss from Purchasing the Put Option (PE) - The terminal value shows the worth of the call option on the exercise date. - The buyer of a call option will have to pay the price of the option at the time of buying. Therefore, the gain from buying a call would be the difference between the terminal value and the price paid for the option. - Thus, gains and losses from buying a call option can be written as: $GC = Max[(ST - SX - CO), -CO]$, where CO is the price paid for the option. - If the option is exercised, - the share price will be higher than the exercise price and the gain would depend on the extent to which the share price is higher than the exercise price. - If the difference between the share price and the exercise price is less than the price paid for the option, the call buyer would still make a loss. - If the difference between the share price and exercise price is more than the price paid for the option, the call buyer will start making profits. - If the option is not exercised, the call buyer will lose the entire amount they paid for buying the call option, which is CO. Therefore, the maximum loss for the option buyer will be CO, which is incurred only upon failure to exercise. ### Gains or Losses from a Call Option (CE) Writers View - The terminal value of the written call can be written as: $CW,T = Min\ (SX - ST, 0)$ - **Gains and Losses for a Call Writer** - When the call writer writes a call, they receive the option price immediately. - The gain or loss on the exercise date will depend on whether the call buyer exercises the call or not. - The gains and losses for a call writer can be written as $GWC = Min\ [CO, CO + (SX - ST)]$, Where CO is the price received while selling of the Call Option ### Comparison Between the Gains Made by a Call Buyer and a Call Writer - **For an option buyer,** - The maximum loss is the option price that they paid for buying the option. - The gain is unlimited (in the sense that it depends on how high the share price can go at the time of maturity). - **For the option writer,** - The gain is the maximum option price that they received at the time of writing the call. - The loss is Unlimited. ### When to Buy and When to Write a Call Option? - When a person buys a call option, they gain only if the share price is expected to increase. - However, the call buyer would make a positive gain only when the share price is more than the sum of the exercise price and the price paid for the option. - If SX is the exercise price and CO is the price paid for the option, a call option would be bought only when the share price ST is expected to be more than (SX + CO), which represents the Break Even Point for the Call Option. - A call writer gains as long as the share price does not go beyond the sum of the exercise price and the option price, or as long as ST is less than (SX + CO). - The belief about the movement of stock prices could be different for the call option writer and the call option buyer. - While the call option buyer always believes that the stock price would increase and go beyond (SX + CO). - The call option writer believes that the stock price may either decrease or even increase and that if it increases, it will not go beyond (SX + CO). ### Value of Call Option Before Expiry - The value of the Call option before maturity is made of two components: - The intrinsic value of the Call option. - The time value of the Call option. $Price\ of\ Call\ =\ Intrinsic\ value\ +\ Time\ value$ ### Put Options - A put option provides the right to sell the underlying security at a fixed price, known as the exercise price, at a specified time in the future, known as the exercise date. - Put options can be of either the American type or European type. - An American put option can be defined as the right to sell an underlying asset at the exercise price on or before the exercise date. - A European put option can be defined as the right to sell an underlying asset at the exercise price on the exercise date only. ### The Terminal Value of a Put Option - The value of a Put option on the exercise date is known as its terminal value. - Consider a European option on the date of maturity. Since it is a European option, it can be exercised only on the exercise date, and in order to decide whether the buyer should exercise or not, it is important for them to know the value of the Put option at that time. - Thus, the terminal value of a Put option is important from that point of view. ### Exercising the Put Option (PE) - It is not profitable to exercise the Put option if the share price on expiry date is higher than the exercise price. - If the share price on expiry date is lower than the exercise price, it is advisable to exercise the Put option. - **Only Buyers of Put Option can Exercise the Put Option.** - If the Share price and the exercise price on the terminal date or expiry date. - **Case 1:** If the exercise price (SX) < terminal stock price (ST), do not exercise; the value of the put option is zero. - **Case 2:** If the exercise price (SX) > terminal stock price (ST), exercise; the value of the put option is (SX - ST). $Terminal\ value\ =\ (S_X - S_T)\ if\ S_T < S_X$ $Terminal\ value\ =\ 0\ if\ S_T > S_X$ where $S_T$ represents the share price on the option expiration date and $S_X$ represents the exercise price of the option. In shortened form, we can write this as: $Terminal\ value\ =\ Max\ (S_X - S_T, 0)$ ### Gains or Loss from Purchasing the Put Option (PE) - When one purchases a European Put option, they would like to know the profit or loss that will be made on the exercise date, when the Put option is exercised, and when it is not exercised. - Earlier, we saw that the terminal value of a Put option is: $PT = Max\ (SX - ST, 0)$ - The terminal value shows the worth of the Put option on the exercise date. - The buyer of a Put option will have to pay the price of the option at the time of buying. - Thus, gains and losses from buying a Put option can be written as: $GP = Max\ (-PO, SX - ST - PO)$ where PO is the price paid for the option. - If the option is exercised, - the share price will be lower than the exercise price and the gain would depend on the extent to which the share price is lower than the exercise price. - If the difference between the share price and the exercise price is less than the price paid for the option, the put buyer would still make a loss. - If the difference between the share price and exercise price is more than the price paid for the option, the put buyer will start making profits. - If the option is not exercised, the put buyer will lose the entire amount they paid for buying the put option, which is PO. Therefore, the maximum loss for the option buyer will be PO, which is incurred only upon failure to exercise. ### Gains or Losses from a Put Option (CE) Writers View - The terminal value of the written put can be written as: $PW,T = Min\ (ST - SX, 0)$ - **Gains and Losses for a Put Writer** - When the Put writer writes a Put, they receive the option price immediately. - The gain or loss on the exercise date will depend on whether the Put buyer exercises the put or not. - The gains and losses for a Put writer can be written as $GWP = Min\ [PO, PO + (ST-SX)]$, Where PO is the price received while selling of the Put Option. ### Comparison Between the Gains Made by a Put Buyer and a Put Writer - **For an option buyer,** - The maximum loss is the option price that they paid for buying the option. - The gain is unlimited (in the sense that it depends on how high the share price can go at the time of maturity.) - **For the option writer,** - The gain is the maximum option price that they received at the time of writing the Put. - The loss is Unlimited. ### When to Buy and When to Write a Put Option? - When a person buys a Put option, they gain only if the share price is expected to decrease. - However, the Put buyer would make a positive gain only when the share price is less than the sum of the exercise price and the price paid for the option. - If SX is the exercise price and PO is the price paid for the option, a put option would be bought only when the share price ST is expected to be more than (SX - CO), which represents the Break Even Point for the Put Option. - The belief about the movement of stock prices could be different for the Put option writer and the Put option buyer. - While the Put option buyer always believes that the stock price would decrease and go below (SX - PO). - The Put option writer believes that the stock price may either increase or even decrease and that if it decreases, it will not go below (SX - PO). ### Value of Put Option Before Expiry - The value of the put option before maturity is made of two components: - The intrinsic value of the put option. - The time value of the put option. $Price\ of\ put\ =\ Intrinsic\ value\ +\ Time\ value$