MBA Introduction Options 2nd Year Long Model Paper
MBA Introduction Options 2nd Year Semester IV Long Sample Model Paper
Introduction to options, Hedging with currency options, Speculation and Arbitrage with options, Pricing options, General principles of pricing, Black- Scholes option pricing model, Index options, Hedging with index options, Speculation and Arbitrage with index options, Index options market in Indian stock market, Use of different option strategies to mitigate the risk.
LONG ANSWER QUESTIONS
Ques.1. Discuss the general principles of option pricing in brief.
Ans. General Principles of Option Pricing The option pricing principles explore the relationship between options which differ by ex price alone as well as those that differ only by time to expiration. The basic principles comprise of rational people behave when they are faced with risky situations. The collective behaviour of rau investors operates in an identical manner so as to determine the fundamental principles of option
Factors Determining Option Price: The price at which the stock under option may be put or called is termed as the contract price. Sometimes, it is also referred to as the striking price. During the life of the contract, the contract price remains fixed, except that market practice is for the contract price which is to be reduced by the amount of any dividend paid or by the value of any stock right which becomes effective during the life of the contract. In purchasing an option, the amount that the buyer pays for the option privilege is called the premium, or sometimes the option money.
The factors which determine the price of option are as follows:
- Expiration Date: The expiration date of the option also affects the premium. The odds of a stock making a profitable move increase with time. The option buyer resembles a brand jumper. The longer is the run, the better will be the chances of making a good jump. Because buyers benefit from the extended periods of time and sellers suffer, buyers or sellers agree towards higher premiums for longer lasting options. For this reason, options are a wasting asset.
- Volatility: Option premiums deflect the personal beliefs of both buyers and sellers. Buyers of options thrive on changes in stock prices and they gladly pay premium for options on volatile stocks. The more the stock prices fluctuate in the future, the better will be their chances for making money and the buyer’s losses also, are limited to the amount of the premium. On the other hand, sellers detest volatility, since it can only work against them. As a result, option sellers usually demand much higher prices for writing options on volatile stocks. The willingness of buyers to pay higher premiums combined with the reluctance of sellers to write them produces higher premiums on the options of more volatile stocks.
- Dividends: Dividends also affect option premiums. Generally speaking, firms paying high dividends seldom increase very much in price. So, prospective call buyers avoid options on their stocks, Since options writers collect these dividends in addition to their premium income, they naturally! prefer to write options on high dividend stocks. Buyers and sellers compromise and agree towards lower premiums for high-dividend paying stocks.
- Striking Prices: Striking prices add a further complication to the analysis of options. The striking price remains the same during the entire life of the option contract. The nearer the striking price is to the market price of the underlying stock, the greater will be the buyer’s chances of making money on the option.
- Interest Rates: Interest rates have an opposite impact on premiums. At higher interest rates, options writers sacrifice a considerable part of income by holding stocks instead of bonds. As a result, they usually demand and get higher premiums for writing option during the times of high interest rates.
Ques.2. What are currency options markets? Explain the hedging with currency options along with the cases of price decline and price increment.
Ans. Currency Options Markets
A currency option gives the buyer, the right but not the obligation, to buy or sell a specific amount! of currency at a specific exchange rate, on or before a specific future date where a premium is due.
Foreign currency options are available on the over-the-counter market as well as on organised exchanges.
- Over-The-Counter (OTC) Market: Over-the-counter options are written by financial institutions, These OTC options are more liquid as compared to forward contracts. At any moment, the holder can sell them back to the original writer, who quotes to-say prices. The main advantage of OTC options is that they are tailored to the specific needs of the firm. Financial institutions are willing to write or buy options that vary by contract size, maturity and strike price.
As a consequence, the bid-ask spread in the OTC market is higher than in the traded-options market. Firms which are buying and selling currency options as part of their risk management program do so primarily in the OTC market. In OTC markets, most of the options are written at a strike price equal to the spot price of that moment (at-the-money options).
Exchange Trade Options: Options on the underlying currency are traded on a number of organised exchanges world wide, including the Philadelphia Stock Exchange (PHLX) and the London International Financial Futures Exchange (LIFFE).
An organised option exchange, just like a clearing-house as a guarantor, i.e. exchange traded option are settled through clearing-house, so buyers do not deal directly with sellers. The clearing-house is the counterpart to every option contract and it guarantees for fulfilment. In the case of the Philadelphia Stock Exchange, the clearing-house is the Options Clearing Corporation (OCC).
Hedging with Currency Options:
Hedging represents a strategy by which an attempt is to be made in order to limit the losses in one position by simultaneously taking a second offsetting position. This offsetting position may be in same or different security. In most of the cases, hedgers are not perfect because they cannot eliminate all losses. Typically, a hedge strategy strives to prevent large losses without significantly reducing the gain.
The hedging strategies to be used against a price rise/decline are as follows:
- Hedging through Purchase of Options: In order to hedge their foreign exchange risks, if it is a direct quote, the importers buy a call option while the exporters buy a put option.
- Hedging through Selling of Options: Hedging through selling of options is advised in case volatility in exchange rate is expected to be only marginal. The importer sells a put option and while the exporter sells a call option.
Hedging Against a Price Decline
Hedging against a price decline can be carried out through the following:
- Put Bear Spread: This is the result of a short one put option at a lower strike price and long one put option at a higher strike price. A put bear spread has the same pay-off as the call bear spread since both strategies hope for a decrease in market prices. The choice regarding which spread to use, however, comes down to risk/reward.
(a) Bear put spread is created by buying a put option at a particular strike price and simultaneously selling a put option with a lower strike price within the same contract month.
(b) A bear put spread should be used in case the marketer is bearish on a market down to a certain point.
- Call Bear Spread: This is the result of a short one call option having a low strike price and a long one call option with a higher strike price. A call bear spread is usually a credit spread which is the case where the net cost of the position results in receiving money upfront for the trade. Such a spread is used when one is mildly bearish on market direction.
- Strips: A strip refers to a long position having one call and two puts options having the same strike price as well as the expiration date.
- Short Minimum Maximum Option Strategy: This strategy is the same as the range forward or collar. In this case, puts are brought with and an equal number of calls are sold with different strike prices having the same expiration date. This strategy establishes minimum and maximum sale prices as well as the range of prices over which the investor will retain some risk but will be able to make some profits. Buying the put option provides the investors with a minimum sales price while still retaining the opportunity to sell the asset at a higher price increase. By selling the calls, the investor fixes the maximum sale price even if cash prices increase in future. The cost of setting up such a strategy is the put premium paid, less the finance from the call premium received. This has the least cost which can be filled with hedger’s desired risk exposure by choosing different put and call prices.
Hedging Against a Price Increment
In this hedging strategy, one has either a short futures position or a short futures position in the cash market. The main purpose is to hedge against a price rise which can be achieved by using the following options contracts:
- Covered Call: This is the result of long the underlying asset and short the call options. This strategy is used by various investors who hold stock. It is also used by many large funds as a method of generating consistent income from the sold options. The idea behind a Covered Call (also called as Covered Write) is to hold stock over a long period of time and every month or so sell out-of-the-money call options.
- Protective Put: This strategy is the result of long the underlying asset and long the put options. A protective put strategy has a very similar pay-off profile to the long call. The maximum loss is limited to the premium paid for the option and can have an unlimited profit potential.
- Put Bull Spread: This is the result of long one put option and short another put option with a higher strike price. A put bull spread has the same pay-off as the call bull spread except that the contracts used are put options instead of call options. Even though bullish, a trader may decide to place a put spread instead of a call spread as the risk/reward profile may be more favourable. This may be if the ITM ca options have a higher implied volatility as compared to the ITM put options. In this case, a call spread would be more expensive to initiate and thus the trader might prefer the lower cost option of a put spread.
- Straps: A strap consists of a long position with two calls and one put option with the same strike price as well as the same expiration date. In the strap position, the investor is betting in favour of significant rise in stock prices as compared to fall or downward. For this, he goes for two call options along with one put option.
- Call Bull Spread: This is the result of a short one call option having a low strike price and long one call option having a higher strike price. A call bear spread is usually a credit spread which is the case where the net cost of the position results in receiving money upfront for the trade. This type of spread is used when the investors are mildly bearish on market direction.
Ques.3. Discuss the speculation and arbitrage with currency options.
Ans. Speculation with Currency
Options A speculator has a definite outlook for future prices and thus buys put or call options depending upon this perception. If he has a bullish outlook, he will buy calls or sell puts. As a bearish perception, the speculator will buy put and write calls. ‘He will earn a profit if his view is in the right direction but if he is not, he will lose the money. A speculator buys call or put options in case his price outlook in a particular direction is very strong.’ But if he is either neutral or not so strong, then he would prefer to write a call or a put option to earn the premium. There are four basic option positions for a speculator, depending on the price outlook that he has of the market.
The speculating with currency options are as follows:
- Spreads: In a spread, speculators combine either two calls or two puts. In case of two calls or puts, one is sold while the other is purchased. If the expiry of the two is the same but the strike prices are different, it is known as a vertical spread. When the strike price is the same but the expiry is different, It is known as a horizontal spread. When the strike price and the expiry date both are different between The two calls, it is known as a diagonal spread. Similar features are marked with two puts.
- Purchase of Options: Speculators make profit out of purchase of currency options. They mally buy call options when they expect upward movement in the value of the underlying currency. on an expiry date, they buy the currency at the agreed-upon rate and sell it in the open market at a rate and thus reap profits. On the contrary, they buy put options when they expect depreciation at a higher rate and some of the underlying cut than the spot rate. The underlying currency. They sell the underlying currency at an agreed-upon rate which is higher e spot rate. Thus, they get more of the other currency than they could get in the open market.
Arbitrage with Currency Option
Arbitrage is the trading process of buying in one market and selling it in another market with the goal of earning nearly riskless profits. For option traders, an arbitrage pricing relationship, a trader can buy shares of stock at a stock exchange and then sell those shares synthetically in the options market. A trader, also, can do the reverse by buying shares synthetically in the options market and then selling then in the stock market.
Arbitrage is the opportunity to make risk-free profit by simultaneously buying an underpriced asset and selling it at a market price. Arbitrage has been regarded as the ‘holy grail’ of the capital markets and options arbitrage certainly is the holy grail of free profits for the privileged options traders in case of options trading. Arbitrage in stock trading typical makes use of price differential between exchanges but also the violations in put-call parity between stock options. In fact, options strategies have also been created to take the advantage of specific options arbitrage opportunities.
The only drawback of options arbitrage is that profitable opportunities are hard to come by and they get filled -out extremely fast by computers used by big financial institutions which are monitoring for such opportunities at all times. Even if a profitable opportunity is discovered the commissions involved in such complex options arbitrage strategies usually take all the profits away. Thus, options arbitrage is commonly the realm of professional options traders who are not required to pay broker sees such as market makers and floor traders. Even for obvious options arbitrage opportunities, each position must be expertedly performed by legging into each side of the trade at the best possible prices so as to guarantee the profitability of the positions. Options arbitrage is the use of stock options to reap marginal risk-free profit by locking the value created through price differential between exchange or violation of put-call parity.
Options Arbitrage Mechanics
For arbitrage to work, an inequality in price of the same security must exist. When a security is underpriced in another market, one simply buys the underpriced security in that market who then sell it at the market price in this market simultaneously so as to reap a risk-free profit, i.e. the same concept in options arbitrage with the only difference being in the definition of the term ‘underpriced’. Underpriced’ takes on a much wider spectrum of meaning in case of options trading. A call option can be underpriced in regards to another call option of the same underlying stock, this call option can also be underpriced in regards to a put option and options of one expiration can also be underpriced in regards to options of another expiration. All of these are governed by the principle of put-call parity. When put-call parity is violated, options arbitrage opportunities do exist.
Because options arbitrage works on the basis of differences in the relative values of one option against another, it is known as ‘relative value arbitrage’. Rather than simply buying and selling securities simultaneously so as to perform an arbitrage trade as in stock arbitrage, options arbitrage makes use of complex spread strategies to ‘lock-in’ the arbitrage value and typically wait for the spread to unwind by expiration before reaping the full reward.
Ques.4. What is Black and Scholes option pricing model? Discuss its assumptions.
Ans. Black and Scholes Option Pricing Model
Black and Scholes theory or derivatives pricing theory traces its roots to Bachelier who invented Brownian motion to model options on French government bonds. This work anticipated Einstein’s independent use of the Brownian motion in Physics by five years.
The Black and Scholes model is used to calculate a theoretical call price (ignoring dividends paid during the life of the option) using the five key determinants of an option price which are stock price, strike price, volatility, time to expiration and short term (risk-free) interest rate.
The original formula to calculate the throretical Option Price (OP) is as follows:
The variables used are:
S = Stock price,
E = Strike price,
t = Time remaining until expiration, which is expressed as a percent of a year,
r = Current continuously compounded risk-free interest rate.
=Annual velocity of stock price (the standard deviation of short-term returns over one year
In = Natural logarithm,
e = Exponential function.
Assumption of Black and Scholes Options Pricing Model
following are the assumptions of Black and Scholes Model:
1.European Exercise Terms: European exercise terms dedicate that the options can only be exercised on the expiration date. American exercise terms allow the options to be exercised at any time during the life of the option, thus making American options more valuable due to their great flexibility This limitation is not a major concern because very few calls are ever exercised before the last few days.This is true because when the investor exercises a call early, he forfeits the remaining time value. Towards the end of the life of a call, the remaining time e is very small but the intrinsic value is the same.
- No Commissions are Charged: Usually market participants have to pay a commission to buy or cell options, even floor traders pay some kind of fee but it is usually very small. The fees that individual westor’s pay are more substantial and they can often distort the output of the model.
- Markets are Efficient: This assumption suggests that people cannot consistently predict the direction of the market or an individual stock. The market operates continuously with share prices following a continuous process
- Stock Pays no Dividends during the Option’s Life: Most of the companies pay dividends to their shareholders, so this might seem a serious limitation to the model considering the observation that higher dividend yields elicit lower call premiums. A common way of adjusting the model for such a situation is to subtract the discounted value of a future dividend from the stock price.
- Returns are Normally Distributed: This assumption suggests that the returns on the underlying stock are normally distributed, which is reasonable for most assets which offer options
- Interest Rates Remain Constant and Known: The Black and Scholes model uses the risk-free rate to represent this constant and known rate. In reality, there is no such thing as the risk-free rate, but the discount rate on US Government Treasury Bills with 30 days left until maturity is usually used to represent it. During the periods of rapidly changing interest rates, these 30 days rates are often subject to change, thereby violating one of the assumptions of the model.
Ques.5. Describe the arbitrage with index options.
Ans: Arbitrage with Index Options
The arbitrage with index options can be done through the following ways:
- Put Call Parity Violation: When an investor buys an asset with a spot price paying ‘S amount, he buys a put at Paying an amount ‘P, so his downside of below X is taken care of (If S < X, he will exercise the put). The investor sells a call at X earning an amount C, so if S > X, the call holder may exercise on him, so his upward beyond X is gone. This may give X on maturity T with certainty. This means that the portfolio of (S+P-C) is nothing but the zero coupon bond which pays Xon date T. What happens in case the above equation does not hold well, it gives rise to arbitrage opportunity?
The put call parity basically, explains the relation between call, put, stock and bond prices. It is expressed as.
S = Current index level,
P= Price of put option,
X = Exercise price of option,
T = Time to expiration,
C = Price of call option,
R = Risk-free rate of interest,
The above expression basically means that the off from holding a call plus an amount of cash equal to X/(1 + R)t), is the same as the holding of put option plus the index.
- Beyond Option Price Bounds: The value of an option before expiration depends on the following six factors:
- The exercise price of the option,
- The level of the underlying index,
- The volatility of the index,
- The risk-free rate of interest,
- Dividends expected during the life of the option,
- The time to expire.
These factors set general boundaries for possible option prices. If the option price is above the upper bound or below the lower bound, there are profitable arbitrage opportunities. An investor shall try to get an intuitive understanding about these bounds.
Upper Bounds for Calls and Puts: A call option gives the holder the right to buy the index for a certain price. No matter what happens, the option can never be worth more than the index. Hence, the index level is an upper bound to the option price.
If this relationship is not true, an arbitrageur can easily make a riskless profit by buying the index and selling the call option.
It is known that a put option gives the holder the right to sell the index for X. No matter how low the index becomes, the option can never be worth more than X. Hence,
If this is not true, an arbitrageur would make profit by writing puts.
Lower Bounds for Calls and Puts: The lower bound for the price of a call option is given by S-X (1+r). The price of a call must be worth at least this much else, it will be possible to make riskless profits.
S-X (1+r)-T < C
Ques.6. Define put call parity. Explain the put call parity for dividend paying stock and correlate it with American style options.
Ans.Put Call Parity
Put call parity is a financial relationship between the price of a put option and a call option with the same characteristics (strike price and expiration date). The put call parity is a concept related to European call and put options. The put call parity is an option pricing concept which requires the values of call and put options to be in equilibrium to prevent arbitrage.
Put Call Parity for Dividend Paying Stock: To understand the effect of dividends on options, first It is required to understand how dividends influence stock prices. If the markets for options, bonds, and stocks are frictionless, ie if there are no transaction costs, no taxes, and no restrictions on short Sales, then it can be shown that stock price must decrease by the amount of the dividends on the ex-dividend date. This is because shareholders who purchased these shares on or after the ex-dividend date are not eligible to receive the announced dividends.
Let us assume that the option expiration date is T and the stock pays a known dividend of D at time t1 with t1<T.
For example, an option may mature in 90 days and the stock may pay dividends after 45 days.
When the options are not protected against dividends, the price of the stock is expected to decrease by the amount of dividend D at the ex-dividend date t1. This will cause the value of the call to decrease and the value of the put to increase. When the dividend payment D and the ex-dividend date are known with certainty, the put call parity relationship is given by:
Put call parity does not hold for American style options
Put call parity does not hold for American style options because American options allow early exercise prior to expiration. However, American options can be exercised at any time until their maturity, and this fact makes deriving the relationship between American calls and American puts more difficult.
Even though a precise relationship between American call and American put cannot be derived because of the possibility of an early exercise, a limit on the put price for a given call price can be derived.
The put call parity is a closed-end concept in which one defines his starting point and knows the outcome at the end. American style options are a problem in this concept as they bring uncertainty into the model. With American style options, one of the options legs in the trade may disappear prior to expiration because of an exercise. Closing the whole trade at this point produces a gain or a loss that is unknown when the option position in initiated. Not closing the position leaves the investor exposed.
Ques.7. What are the assumptions and mechanisms of put call parity?
Ans. Assumptions of Put Call Parity Put call parity
Put call parity is based on the following assumptions:
- The dividends to be received are known and certain,
- The underlying stock is highly liquid and no transfer barriers exist, and
- Interest rate does not change in time, but it is constant for both borrowing and lending.
Mechanisms of Put Call Parity: Prices of put options, call options, and their underlying stock are very closely related. A change in the price of the underlying stock affects the price of both call and put options that are written on the stock. The put call parity defines this relationship. The put call parity relationship is specific in a way that a combination of any of the two components yields the same profit or loss profile as the third instrument. The put call parity says that if all these three instruments are in equilibrium, then there is no opportunity for arbitrage.
The relationship is derived from the fact that combinations of options can make portfolios that are equivalent to holding the stock through time T, and that they must return exactly the same gain or loss or an arbitrage would be available to the traders. The concept of put call parity is especially important in case of trading synthetic positions. When there is a mispricing between an instrument and its synthetic position, the put call parity implies that an options arbitrage opportunity exists.
The put call parity can be described as follows:
P (s, t) +S (t) =C (S, 6) + Ex B(t)
and can be expanded into
P (S, t) +S(t) = C (S, t) + Exe MT
P (S, t) = Price of the put option when the current stock price is S and the current date is t,
S(t) = Stock’s current price,
C (S, t) = Price of the call option when the current stock price is S and the current date is t,
E =Strike price of the put option and call option,
B(t) = Price of a risk-free bond,
r = Risk-free interest rate,
t = Current date,
T = Expiration date of a put option and a call option.
The put call parity is a representation of two portfolios which yield the same outcome.
Put option + Stock = Call option + Bond
The left side represents a portfolio consisting of a put option and a stock. The right side represents a portfolio consisting of a call option and a bond. If the price of the underlying stock rises, the put option expires worthless, the stock gains value, the call option ends in money and the bond earns a risk-free rate. Both portfolios have equal value at the end. Regardless of whether the price of the underlying stock grows or falls, both sides of the equation balance each other. If a portfolio on one side of the equation was cheaper, one could purchase it and sell the portfolio on the other side adn profit from a risk-free arbitrage
Ques.8. Discuss about index options market in Indian stock market.
Or Write a detailed note on index options market in Indian stock market.
Ans.Index Options Market in India in Stock Market
India has a long history in security exchanges, derivative trading in the National Stock Exchange (NSE) and the Bombay Stock Exchange (BSE) started only in 2000. The trading of derivatives in India started in June 2000 on the National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) with index futures. Subsequently the trading of index options and options on individual securities started in June 2001 and July 2001. The commencement of single stock futures was in November 2001. Since then the underlying asset base has increased to include trading in futures and options on Bank Nifty Index, CNX IT Index, and Nifty Midcap indices, etc. At present, both in terms of turnover and volume. NSE is the major derivatives exchange in India.
All the options which have an index as underlying are known as Index Options. The two most basic and popular index options are Call Option and Put Option. Further, they may be American Options or European Options.
Many different index options are currently traded on the different exchanges in different countries. For example, S&P 100 index at CBOE and major index at AMEX are traded in the US option markets. Similarly, in India, such index options have been started on the National Stock Exchange and Bombay Stock Exchange. Like stock options, index options strike prices are the index values at which the buyer of the option can buy or sell the underlying stock index. The strike index is converted into dollar (rupee) value by multiplying the strike index by the multiple for the contract.
The money value of the stock index underlying an index option is equal to the current cash index value multiplied by the contracts multiplied.
Rupees value of the underlying index = cash index value x contract multiplies
On NSE’s index options market, there are one-month, two-month and three-month expiry contracts with minimum nine different strikes available for trading. Hence, if there are three serial month contracts available and the scheme of strikes is 6-1-6, then there are minimum 3 x 13 x 2 (call and put options), i.e, 78 options contracts available on an index. Options contracts are specified as follows:
For Example, the European style call option contract on the Nifty index with a strike price of 2040 expiring on the 30 th June 2005 is specified as ‘30 JUN 2005 2040 CE’.
Just as in the case of future contracts, each option product (e.g. the 28 June 2005 2040 CE) has its own order book and own prices. All index options contracts are cash settled and expire on the last Thursday of the month. The clearing corporation does the innovation. The minimum tick for an index options contract is 0.05 paise.
Table: Contract Specification: S&P CNX Nifty Options
|Underlying Index||S&P CNX Nifty|
|Exchange of Trading||National Stock Exchange of India Limited|
|Security Descriptor||OPTIDX NIFTY|
|Contract Size||Permitted lot size shall be 50 (minimum value 2 lakh|
|Price Steps||0.05 paise|
|Price Bands||Not applicable|
|Trading Cycle||The options contracts will have a maximum of three month trading cycle- the near month (one), the next month (two) and the far month (three). New contract will be introduced on the next trading day following the expirey of near month contract.|
|Expiry Day||The last Thursday of the expiry month or the previous trading day if the last Thursday is a trading holiday.|
|Settlement Basis||Cash settlement on T + 1 basis.|
|Style of option||European|
|Daily Settlement price||NA|
|Final Settlement Price||Closing value of the index on the last trading day of the options contract.|
Ques.9. A 2-month call option on Infosys with a strike price of 3,100 is selling for 150 when the share is trading at 3,200. Find out the following:
- What is the intrinsic worth of the call option?
- Why should one buy the call for a price in excess of intrinsic worth?
- Under what circumstances the option holder would exercise his call?
Sol. 1. The intrinsic worth of the option is (S – X) = 3,200 – 3,100 = 7100
- The price of the option is 150, i.e., 40 more than the intrinsic worth. This is the time value of the option and is paid because there are chances that in the next two months, the price of Infosys may rise further and holder stands to gain a greater amount than 100, the present intrinsic worth.
- The option holder would exercise his call if the price of the asset, S > X, the exercise price, i.e., when S > 3,100.
Ques.10. A 3-month put option on the Tisco Steel with a strike price of 3 550 is selling for 60 when the share is trading at 500. Find out the following:
- What is the intrinsic worth of the put option?
- What is the time value of the put option?
- What interpretation can you attach with the time value?
- At what price of the asset the put option holder would break even?
Sol. 1. The intrinsic worth of the option is (X – 5) = 550 – 500 = 50.00.
2.The time value of put is option price less its intrinsic worth = 60 – 50 = 10.00
- The time value is paid by the buyer of the option that the intrinsic value of the option may rise in future with the fall in the prices. As the price of the underlying falls, the put options becomes more in the money and therefore the holder stands to gain a greater amount.
- If the value of Tata Steel shares falls to 490, the put option holder would get back the entire premium by way of intrinsic worth of the option. However, instead of exercising the option, he may like to sell the same as it would fetch a greater value, the time value over and above the intrinsic value.
Q.11. A two month Nifty call option with a strike of 1260. Nifty stands at 1350. The risk-free rate of interest is 12% per annum. Arbitrage opportunities will arise when the call premium falls below at what price?
Sol. The lower bound for a call option is given by S – X (1+r)-T
This works out to be 1350 – 1260 (1 +0.12)-0.166 = 113.50
Q.12. Three put options X, Y, and Z with strike prices of 100, 105, and 110 are selling at 2,75, and 13 respectively, when the underlying stock is trading at 105.
- Find out which of the put options are ITM, ATM, and OTM.
- If the price of each of the put options increases by 1, would your answer to moneyness of options change?
- If the price of each of the options decreases by 1, what would be the change in the moneyness of each of the options?
Sol. 1. Moneyness of put options is as under:
Option X:X-S=100 – 105 = Negative; Out-of-the-money by 5
Option Y:X-S= 105 – 105 = Zero; At-the-money
Option Z:X-S=110 – 105 = Positive; In-the-money by 5
- and 3. If the price increases or decreases there would be no change in the moneyness of options, Premium paid is a sunk cost.
Ans. Q.13. Ashish is bullish about the index. Spot Nifty stands at 1200. He decides to buy one three month Nifty call option contract with a strike of 1260 at a premium of 15 per call. Three months later, the index closes at 1295. What will be his pay-off on the position?
Sol. Each call option earns him (1295 – 1260 – 15) 200 = 20 x 200 = 4,000.