MBA Introduction Options 2nd Year Short Sample Model Paper

MBA Introduction Options 2nd Year Semester IV Short Sample Model Paper

MBA Introduction Options 2nd Year Semester IV Short Sample Model Paper

MBA Introduction Options 2nd Year Short Sample Model Paper
MBA Introduction Options 2nd Year Short 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.

section B

SHORT ANSWER QUESTIONS

Ques.1. Discuss the various types of options with examples.

Ans. Types of Options: Basically, there are two types of options:

  1. Call Options

In call options, the option buyer has the right (but not the obligation) to buy the commodity at the predetermined price (in a sense, “call for the item from the market, hence the term).

A call option is purchased in hope that the underlying stock price will rise well above the strike price, at which point one may choose to exercise the option. Exercising a call option is the financial equivalent of simultaneously purchasing the shares at the strike price and immediately selling them at the now higher market price.

For example, A enters into a contract with B whereby A has the right to purchase 100 ounces of gold from B for $400 per ounce at any time prior to August 1. For granting this option, A pays Ban option premium of $5 per ounce. This is a call option.

Example: Tom House paid a premium of 4 per share for one 6-month call option contract (total of 400 for 100 shares) of the Mahoney Corporation. At the time of the purchase, Mahoney stock was selling for 56 per share and the exercise price of the call option was 55.

  1. Determine Tom’s profit or loss if the price of Mahoney’s stock is 754 when the option is

Exercised?

  1. What is Tom’s profit or loss if the price of Mahoney’s stocks 62 when the option is exercised?

Ignore taxes and transaction cost.

Solution:

  1. Cost of call = 4 premium) x 100 = 400

Ending value = (-3400 cost) + (O gain) = 400 loss

The option was worthless because the stock’s price is less than the exercise price at maturity.

  1. Cost of call=400

Ending value =-3400+ ( 62-755) x 100=-*400+700 = 300 gain

  1. Put Options

Input options, the option buyer has the right to sell the commodity (in a sense, ‘put ‘the commodity in the market). A put option is purchased in hope that the underlying stock price will drop well below

the strike price, at which point one may choose to exercise the option. For example, A enters into a contract with B whereby he has the option to sell 100 ounces of gold to B at a price of $400 anytime before August 1. For granting him this option, A pays B $6 per ounce as premium. This is a put option

Example: Anand is bearish on the stock of the Mahesh Corporation. Therefore, Anand purchases four put option contracts on Mahesh stock for a premium of 3. The option’s striking price is ? 40 and it has a maturity of 3 months. Mahesh has a current market price of 39. If Anand is correct and Mahesh’s price falls to 330, how much profit will he earn over the 3-month period? Ignore transaction cost and taxes.

 Solution: Cost of put= 3 per share) x (100 shares per contract) (4 contracts) 1.00! Put’s intrinsic value=Striking price – Ending price = (40-30) = 10 per share Total value at maturity = 10 per share) x (100 shares) (4 contracts) = 4.000 Net gain = 4,000 – 1,200 = 2,800

Ques.2. Explain American and European options.

Ans. American Options: American options are options that can be exercised at any time unto the expiration date. Most exchange-traded options are American. Most of the options that teada organised exchanges are American options. For example, the Chicago Board Options Exchange (CBOE)  trades American options, primarily on stocks and stock indexes like the S&P 100 and the S&P 500. European options traded from the mid 1980s through 1992 on the American Stock Exchange and are often traded in the over-the-counter market as well. The American Stock  Exchange reintroduced them in the late 1990s.

European Options: European options are options that can American options because they can be exercised only on the expiration date itself. European options are easier to analyse than American options and properties of an American options are frequently deduced from those of its European counterpart.

European options are easier to value than American options because the analyst’s need only be concerned about their value at one future date. Both European and American options have the same value. Because of their relative simplicity and the understanding of European option, valuation is often the springboard to understanding the process of valuing the more! popular American options.

For example, all the other facts are as above, but the option is a European option. In this case, A cannot exercise the option on May 15 because he only has the right to do so on the maturity date. He therefore, does not have the profit opportunity.

It will be clear that an American option has a greater profit potential than a European option for the buyer. This leads to premia being higher for American option.

Ques.3. What are the advantages and disadvantages of options?

Ans. Advantages of Options: The advantages of option trading are as follows:

  1. Time to Decide: By taking a call option, the purchase price for the shares is locked-in. This gives! the call option holder until the expiry day, to decide whether or not to exercise the option and buy the shares.
  2. Leverage: Leverage provides the potential to make a higher return from a smaller initial outlay than investing directly. However, leverage usually involves more risks than a direct investment in the underlying shares.
  3. Income Generation: One can earn extra income over and above dividends by writing call options against the shares, including shares bought using a margin lending facility. By writing an option, one receives the option premium up front.
  4. Diversification: Options can allow to build a diversified portfolio for a lower initial outlay than purchasing shares directly.
  5. Risk Management: Put options allow hedging against a possible fall in the value of shares one hold.
  6. Speculation: The ease of trading in and out of an option position makes it possible to trade options with no intention of ever exercising them. If one expects the market to rise, he/she may decide to buy call options.

Disadvantages of Options:1. disadvantages of options are as follows:

  1. Complex Process: Understanding option trading requires great observation and maintenance.
  2. Lower Liquidity: With the wide range of prices available, some will suffer from very low liquidity making the trading difficult.
  3. Costly: The cost of trading options including both commissions and the bid is higher on a percentage basis than trading the underlying stock.
  4. Time Decay: Option trading is time-sensitive in nature and leads to the result that the most options trading expire worthless. This is only applied to the traders that purchase options.
  5. High Risk: Options, like any financial product, obey the risk/reward ratio. The higher is the potential reward, the higher will be the potential risk and vice versa.

Ques.4. Explain the various components of options pricing,

Ans. Components of Options Pricing: The total value of an option consists of intrinsic value, which is simply how far in-the-money an option is, and time value, which is the difference between the price paid and the intrinsic value. Thus,

Option price = Intrinsic value + Time value

  1. Intrinsic Value: The intrinsic value of an option is the difference between the actual price of the underlying security and the strike price of the option. Both call option and put option have intrinsic value.

(a) Intrinsic Value of a Call Option: When the underlying security’s price is higher than the

strike price, a call option is said to be ‘in-the-money

(b) Intrinsic Value of a Put Option: If the underlying security’s price is less than the strike price, a put option is ‘in-the-money. Only in-the-money options have intrinsic value, representing the difference between the current price of the underlying security and the option’s exercise price, or strike price.

The intrinsic value of an option reflects the effective financial advantage which would result from the immediate exercise of that option.

Conditiion Call Put
Strike price < Underlying security price In-the-money

Intrinsic value > 0

Out-of-money

Intrinsic value=0

Strike price > Underlying security price Out-of-the-money

Intrinsic value = 0

In-the-money

Intrinsic value > 0

Strike price = Underlying security price At-the-money

Intrinsic value=0

At-the-money

Intrinsic value=0

Time Value: Prior to expiration, any premium in excess of intrinsic value is called time value. Time value is also known as the amount that an investor is willing to pay for an option above its intrinsic value, in the hope that at some time prior to expiration, its value will increase because of a favourable change in the price of the underlying security. It is determined by the remaining lifespan of the option, the volatility and the cost of refinancing the underlying asset (interest rates). So,

Time value = Option price – Intrinsic value

The option premium is always greater than intrinsic value. This extra money is for the risk which the option writer/seller is underlying. The longer is the amount of time for market conditions to work to an investor’s benefit, the greater will be the time value.

Ques.5. Write the differences between options and futures.

Ans.                                 Differences between Options and future

S.No Basis of difference Options Futures
1 Meaning Options confer the right but not the obligation on buyers to buy or sell foreign currencies. Futures oblige buyers to buy or sell foreign currencies (unless the contract has been sold prior to maturity.)
2 Consideration An option buyer pays the seller an option price. A future buyer does not pay the seller to accept the obligation.
3 Obligation to contract One party to an option contract is not obligated to transact at a later date. Specifically, the option buyer has the right but not obligation to perform. The option writer (seller) though, does have the obligation to perform, if the buyer of the option insists on exercising its. In the case of a future contract, both buyer and seller are obligated to perform.
4 Margin requirement Options, which are paid for at the outset of the contract, do not attract margin requirements. Futures attract margin requirements (security deposits).
5 Maturity Options (American) may be exercised at any time up to the specified maturity date. Futures are fulfilled only on specified maturity dates.
6 Versatility An option trading is a lot more versatile than futures trading as the unique combination of call options and put options along with premium on each contract made it possible for options strategies that profit in all directions. Apart from arbitraging, a future trading is basically single directional (one can make money only when price moves in one direction).
7 Risk protection Investor can use options to protect against asymmetric risk. Investor can use futures to protect against symmetric risk.

Ques.6. Illustrate the applications and advantages of currency options.

Ans. Applications of Currency Options: Following are the applications of currency options:

  1. Importers seek to protect and minimize costs.
  2. Issuers, who have benefitted from having raised funds or leased low interest rate currency that subsequently weakens beyond a fully hedged break-even rate and holds prospects of further depreciation.
  3. Exporters seek to protect and maximize the value of foreign currency denominated revenues.
  4. Companies hold rights to purchase foreign currency denominated goods.
  5. Corporations are planning investments, acquisitions or divestiture.
  6. Any firm facing foreign currency denominated obligation or revenue contingent upon other business factors,

Advantages of Currency Options: The advantages of currency options are as follows:

  1. Options also provide a cover against contingent currency exposures. If such exposures are, covered in the forward market and then it does not materialize, the businessman is left with the negative exposures of the forward contract,
  2. Currency options provide cover  exporters and importers and protects against downside risk. Thus, their cash flows are protected.
  3. Currency options also provide a cover against adverse currency movements that might affect the value of assets and liabilities in a balance sheet.

4.The currency option can also be resold for their residual value

Ques.7. Write basic options positions for speculation.

Ans. The basis options positions for speculation are given below:

  1. Long Call (Buy Call): A long call is simply the purchase of one call option: Along call option is ha simplest way to benefit if we believe that the market will make an upward move and is the most common choice among first time investors: Being long, a call option means that we will benefit if the Shock/future rallies, however, our risk is limited on the downside if the market makes a correction,
  2. Long Put: A long put is simply the purchase of one put option. Like the long call, a long put is a simple way to take a position on market direction without risking everything: Except with a put option, the investor wants the market to decrease in value. Buying put options is a fantastic way to profit from a down turning market without shorting stock. Even though both methods will make money if the market sells off, buying put options can do this with a limited risk
  3. Short Call: A short call is simply the sale of one call option. A selling option is also known as “writing an option. A short is also known as a naked call. Naked calls are considered very risky positions because the risk is unlimited.
  4. Short Put: A short put is simply the sale of a put option. Like the short call option, selling naked puts can be a very risky strategy as our losses are unlimited in a falling market. The written put can provide the investor with extra income (premium received on put option) in stable to rising markets. Most investors use this strategy as a method of buying stocks at a cheaper rate. Short put is used when the investor expects the share price/index to remain steady or be slightly bullish over the life of the option.

Ques.8. What are the main methodologies for options arbitrage?

Ans. The main methodologies for options arbitrage is as follows:

  1. Strike Arbitrage: Strike arbitrage takes advantage of abnormally high extrinsic value through simultaneously buying and selling options of the same underlying stock and expiration but at different strike prices. When the difference in extrinsic value yield exceeds the difference in strike prices, a risk free options arbitrage trade is formed.
  2. Calendar Arbitrage: Calendar arbitrage takes advantage of abnormally higher extrinsic value of nearer term options than longer-term options through simultaneously selling the nearer term option and buying the longer-term option of the same strike price. Such conditions are extremely rare as longer-term options typically have much higher extrinsic value than nearer term options.
  3. Intra-market Arbitrage: Intra-market arbitrage is exactly what stock traders do for stock

arbitrages. It is where the same option is sold for slightly different prices in different exchanges.

  1. Conversion and Reversal Arbitrage: Conversion and reversal arbitrage works when a price difference between the stock and its synthetic equivalent exists. By selling the underpriced of the two and then simultaneously buying the overpriced, risk-free profit can be obtained.
  2. Box Arbitrages: Box arbitrage or Box conversion, is an options arbitrage strategy taking advantage of discrepancies across both call and put options of different strike prices by ‘boxing in the profit using a 4 legged spread. This is also known as a box spread.
  3. Dividend Arbitrage: Dividend arbitrage makes use of lower cost of hedging in order to lock in a higher dividend gain risk-free.

 Ques.10. Discuss about the hedging with index options.

Ans. Hedging with Index Option: Hedging in index options is done by using the way, i.e. have a portfolio, buy puts. Owners of equity portfolios often experience discomfort about the overall stock market movement. An owner of a portfolio, sometimes, may have a view that stock prices will fall in the near future. At other times, he may see that the market is in for a few days or weeks of massive volatility! and he does not have an appetite for this kind of volatility. The union budget is a common and reliable source of such volatility. Market volatility is always enhanced for one week before and two weeks after a budget. Many investors simply do not want the fluctuations of these three weeks. One way to protect! their portfolio from potential downside due to a market drop is to buy portfolio insurance.

Index options are a cheap and easily implementable way of seeking this insurance. The idea is simple. To protect the value of an investor portfolio from falling below a particular level, buy the right number of put options with the right strike price. When the index falls, the investor portfolio will lose value and the put options bought by him will gain, effectively ensuring that the value of his portfolio does not fall below a particular level. This level depends on the strike price of the options chosen by him.

Portfolio insurance using put options is of particular interest to Mutual Funds that already own well-diversified portfolios. By buying puts, the fund can limit its downside in case of a market fall.

Portfolio Insurance when Portfolio Beta is 1.0:

  1. Assume that the investor has a well-diversified portfolio with a beta of 1.0 which he would like to insure against a fall in the market.
  2. Now, he needs to choose the strike at which he should buy puts. This is largely a function of how safe he wants to play. Assume that the spot Nifty is 1250 and he decides to buy puts with a strike of 1125. This will insure his portfolio against an index fall lower than 1125
  3. When the portfolio beta is 1, the number of puts to buy is simply equal to the portfolio value divided by the spot index. Assume his portfolio is worth 1 million. Hence, the number of per he needs to buy to protect his portfolio from a call in index is (10,00,000/1250) which works out to be 800. At a market lot of 200, it means that he will have to buy 4 market lots of month puts with a strike of 1125.

Portfolio Insurance when Portfolio Beta is not 1.0:

  1. Assume that the investor has a portfolio with beta equal to 1.2 which he would like to insure against a fall in the market.
  2. Now he needs to choose the strike at which he should buy puts. This is largely a function of how safe he warns to play. Assume that the spot Nifty is 1200 and he decides to buy puts with a strike of 1440. This will insure our portfolio against an index fall lower than 1140.
  3. For a portfolio with a non-unit beta, the number of puts to buy equals (Portfolio value x Portfolio beta)/Index. Assume our portfolio is worth * 1 million with a beta of 1.2. Hence the number of puts he needs to buy to protect our portfolio from a downside is (10,00,000 x 1.2)/1200 which works out to 1,000. At a market lot of 200, it means that he will have to buy 5 market lots in two months with a strike of 1140.

Ques.11. Explain binomial options pricing model.

Ans. Binomial Options Pricing Model (BOPM): In finance, the binomial options pricing model provides a general sable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein. This model is an important technique of pricing a stock option by constructing a binomial tree. The binomial tree represents different possible paths that may be followed by the stock price over the life of the option. At the end of the tree, i.e. at the expiration of the option, the final possible stock prices are simply equal to their intrinsic values. This model will consider the time to expiry of an option as being one period, two periods and multiple periods.

The binomial model is used with the help of probabilities of a stock moving up or down, the risk-free rate and the time interval of each step in the binomial tree) till expiry. By the use of these probabilities, a binomial tree is to be constructed and evaluated to finally find the price of a call option.

Essentially, the model uses a ‘discrete-time’ model of the varying price over time of the underlying financial instrument. Option valuation is then through the application of the risk neutrality assumption over the life of the option, as the price of the underlying instrument evolves.

Assumptions of BOPM: The assumptions of BOPM are as follows:

  1. The current selling price of the stock (S) can only take two possible values, i.e., an upper value (SJ) and a lower value (Sd).
  2. A perfect and competitive market involves the following:

(a) There are no transaction costs, taxes or margin requirements.

(b) The investors can lend or borrow at the risk-less rate of interest r, which is the only

interest rate prevailing.

(c) The securities are tradable in fractions, i.e., they are divisible infinitely.

(d) The interest rate (r) and the upswing/downswings in the stock prices are predictable. 3. The value of (1+r) is greater than d, but smaller than u, i.e., u < (1 + r) < d. This condition or

assumption ensures that there is no arbitrage opportunity 4. The investors are prone to wealth maximization and lose no time in exploiting the arbitrage Opportunities.

 

Ques.12. Write the advantages and disadvantages of binomial option pricing model.

Ans. Advantages of Binomial Option Pricing Model: Following are the advantages of binomial option pricing model:

  1. It reveals the construction of the replicating portfolio.
  2. It reveals that the probability distribution is not centrally involved, since expectations of outcomes aren’t used to value the derivatives.
  3. The big advantage the binomial model has over the Black Scholes model is that it accurately prices American options. This is because with the binomial model, it is possible Finance to check at every point in an option’s life for the possibility of early exercise (e.g. where to a dividend or a put being deeply in the money, the option price at that point is less than it the sty intrinsic value).
  4. It reveals that we need more probability theory to get a complete understanding of path dependent probabilities of security prices.
  5. It is simple to calculate, although it can get tedious.

Disadvantages of Binomial Option Pricing Model: Following are the disadvantages of binomial is on option pricing model:

  1. The calculations are tedious.
  2. Trading times are not really at discrete times and trading goes on continuously.
  3. Securities do not change value according to a Bernoulli distribution on a single time step, or a binomial distribution on multiple time periods but they change over a range of values with a continuous distribution.
  4. Developing a more complete theory is going to take some detailed and serious limit-taking considerations.

Ques.13. What are the advantages and disadvantages of Black and Scholes option pricing model?

 Ans. Advantages: Advantages of Black and Scholes option pricing model are as follows:

  1. The Black and Scholes model is an attempt to simplify the markets for both financial assets and derivatives into a set of mathematical rules. The model serves as the basis for a wide

range of analysis of markets.

  1. The main advantage of the model is that it works entirely on objective figures rather than human judgment. Another benefit is that, although complex for human calculation, the formula is relatively simple in mathematical terms, so it does not require a sophisticated computer programmed to make calculations,
  2. The main use of the model is to deal with options pricing. An option is a financial contract by which one party buys the right to purchase a designated asset, such as a stock, from the other party on a future date at a price agreed in advance. The option’s value comes from the fact that the market price for the asset may be higher than the agreed price on this date. This will allow the buyer to exercise options, buy the asset and sell it at an immediate profit. This differs from and is far more valuable to the buyer than a futures contract in which the buyer must complete! the deal regardless of the market price on the completion date.

Disadvantages of Black and Scholes Option Pricing Model: The disadvantages of Black and Scholes model are as follows:

  1. It makes several assumptions that are not necessarily true in reality. This includes the fact that even so called risk-free investments, such as government bonds still carry a slim possibility of default.
  2. Another factor is that the pricing doesn’t take account of transaction cost or taxes.
  3. The formula also fails to take account of any dividends which the holder of the underlying asset may receive.

 

Ques.14. Explain the following:

(1) Pay-off of long and short put.

(II) Pay-off of long and short call.

Ans. (1) Pay-off of Long and Short Put: Pay-off of long and short put can be explained by the example of buying and selling a put.

1.Buying a Put: The buyer of a put will gain whenever the price of the asset ends up below the strike price. However, since the buyer has to pay the premium, the gains will arise only after the premium amount has been recovered. If the asset price ends up above the exercise price, the buyer discards the put, resulting in a loss of the premium amount paid. The buyer of an American put can cause this right at any time during the tenure of the contract. Thus, the maximum loss that the buyer incur is only the premium amount. The asset value cannot be negative and the lowest it can reach only 0. In such a case, the buyer will get a gain equaling strike price, i.e., 0. Hence, the maximum gain that the buyer can get, is the strike price.

  1. Selling a Put: The seller of a put will gain whenever the price of the asset ends up above the strike vice. The initial premium gained by the seller will be his total gain in such circumstances. However, if the price of the asset falls below the strike price, the seller will suffer losses. The premium initially received will offset the losses for a small extent, but as the price ends up lower, the seller’s losses are greater. The seller of an American call is exposed to this risk at any time during the tenure of the contract.

Thus, the maximum loss that the seller can incur is the strike price (since the asset value cannot go below 0), while the maximum profit will be the premium received,

(II) Pay-off of Long and Short Call: Pay-off of long and short call can be explained by the example! of buying and selling a call.

  1. Buying a Call: The buyer of a call will gain whenever the price of the asset exceeds the strike! price. However, since the buyer has to pay the premium, the gains will arise only after the premium amount has been recovered beyond the exercise price. If the asset price ends up below the exercise price, the buyer will discard the call, resulting in a loss of the premium amount paid. The buyer of an American call can exercise this right at any time during the tenure of the contract. Thus, the maximum loss that the buyer can incur is only the premium amount, while the maximum profit can be infinite.
  2. Selling a Call: The seller of a call will gain whenever the price of the asset ends up below the strike price. The initial premium that is gained by the seller will be his total gain in such circumstances. However, if the price of the asset exceeds the strike price, the seller will suffer losses. The premium initially received will offset the losses for a small extent, but as the price ends up higher, his losses are greater. The seller of an American call is exposed to this risk at any time during the tenure of the contract. Thus, the maximum loss that the seller can incur is infinite whereas the maximum profit will be the premium received. 0.15. Enumerate the speculation with index options. Ans. The speculation with index options can be done through following ways:
  3. Bullish Index-Buy Nifty Calls or Sell Nifty Puts: There are times when investor believes that the market is going to rise. To benefit from the upward movement in the index, the investor has two choices—Buy call option on the index or sell put option on the index.

Say, e.g., having decided to buy calls, the critical question is which one the investor should buy, given that there are a number of one month calls trading, each with a different strike price. Put premium Call premium Nifty Strike price

Nifty Strike price Call premium Put premium
1250 1200 80.10 18.15
1250 1225 63.75 26.50
1250 1250 49.45 37.00
1250 1275 37.50 49.80
1250 1300 27.50 64.80

Assumption: The current Index is at 1250.

Rf= 12%

Index volatility = 30%

Which of  these options an investor chooses depends largely on how he feels about the likeliber waru movement of the index and how much he is willing to lose, if this upward movement does not come about.

The call with a strike price of 1200 is deep in the money and hence trades at a higher premix The call of 1275 is out of manna and the trade cat a lower premium. The call with 1300 is deep money, hence its execution depends upon the unlikely event of an index rising by more than 50 points the expiration date and thus buying this call is a gamble.

As a person who wants to speculate on the hunch that the market may rise, the investor can also do so by selling or writing puts. As a writer of puts, he has to limit the upside movement and unlimited the downside movement. If the index does rise, the buyer of the put will let the option expire and the investor will earn the premium. If however his hunch about the upward movement of market proves to be wrong and the index actually falls, then the investor incurs losses directly with the falling under

  1. Bearish Index-Sell Nifty Calls or Buy Nifty Puts: An investor sometimes thinks that the market index is going to drop or that he could make a profit by adopting a position on the index. Due to poor corporate results or the instability of the government, many people feel that the index would go down. How does one implement a trading strategy to benefit from a downward movement in the index? Today, to buy using options, an investor has two choices:

(a) Sell call options on the index

(b) Buy put options on the index

The upside to the writer of the call option is limited to the option premium which he receives upright for writing the option. His downside, however, is potentially unlimited. Suppose an investor has a hunch that the market index is going to fall in a months’ time, his hunch proves correct and the index does indeed fall and it is this downside that he cash in on. When the index falls, the buyer of the call lets the call expire and he get to keep the premium. However, if the investor hunch proves to be wrong! and the market index soars up instead, what he lose is directly proportional to the rise in the index.

Nifty Strike price of option Call premium Put premium
1250 1200 80.10 18.15
1250 1225 63.75 26.50
1250 1250 49.45 37.00
1250 1275 37.50 49.80
1250 1300 27.50 64.80

Having decided to write a call, which one should the investor write? The table above gives the premiums for one month calls and puts with different strikes. Given that there are a number of one month calls trading, each with a different strike price, the obvious question is-Which strike should the investor would choose? Let us take a look at call options with different strike prices. Assume that the current index level is 1250, risk-free rate is 12% per year and index volatility is 30%. Investor could write the following options:

(a) A one month call on the Nifty with a strike of 1200.

(b) A one month call on the Nifty with a strike of 1225.

(C) A one month call on the Nifty with a strike of 1250.

(d) A one month call on the Nifty with a strike of 1275.

(e) A one month call on the Nifty with a strike of 1300.

In these options, the investor’s choice largely depends on how strongly he feels about the likelihood of the downward movement in the market index and how much he is willing to lose so that!

downward movement not come about. There are five one-month calls and five one month puts dine in the market. The call with a strike of 1200 is deep in-the-money and hence trades ate higher mum. The call with a strike of 1275 is out-of-the-money and tradesatalow premium. The callosity

IKEA of 1300 is deep-out-of-money, Its execution depends on the unlikely event that the Nullity will Rise by more than 50 points on the expiration date. Hence writing this call is a fairly safe hat. Thane is a small probability that it may be in-the-money by expiration in which case the buyer eventide and the writer suffers losses to the extent that the Nifty is above 1300. In the more likely event off the call aspiring out-of-the-money, the writer earns the premium amount of 27.50.

As a person who wants to speculate on the hunch that the market index may fall, any person can also buy puts. As the buyer of puts, the investor faces an unlimited upside but a limited downside. Tiff the index does fall, he gets the profit to the extent the index falls below the strike of the putt purchased by him. If however his hunch about a downward movement in the market proves to be wrong and the index actually rises, all he loses is the option premium. For example, if the index rises to 1300 and the investor has bought a put with an exercise of 1250, he simply let the put expire. If however the market index does fall to, say, 1225 on expiration date, he makes a neat profit of 25.

Having decided to buy a put, which one should the investor buy? Given that there are a number of one-month puts trading, each with a different strike price, the obvious question is—which strike should the investor choose? This largely depends on how strongly he feels about the likelihood of the downward movement in the market index. If he buys an at-the-money put, the option premium paid by him will be higher than if he buys an out-of-the-money put. However, the chances of an at-the-money put expiring in-the-money are higher as well.

  1. Anticipate Volatility by Buying a Put and a Call (Straddle Strategy): How does one implement a trading strategy to benefit from market volatility? Combination of call and put options provides an excellent way to trade in volatility and this is what an investor needs to do. These are:

(a) Buy call options on the index at a strike Kind maturity T, and

(b) Buy put options on the index at the same strike K and of maturity T.

This combination of options is often referred to as a straddle and is an appropriate strategy for an investor who expects a large move in the index but does not know in which direction the move will be.

  1. Bull Spreads- Buy a Call and Sell Another: There are times when an investor thinks that the market is going to rise over the next two months, However, in the event that the market does not rise, he would like to limit his downside. One way he could do this is by entering into

Option SE a spread: A spread trading strategy involves taking a position in two or more options of the same type, i.e., two or more calls or two or more puts.

How does one go about doing this? This is basically done utilizing two call options having the same expiration date, but different exercise prices. The buyer of a bull spread buys a call with an exercise price below the current index level and sells a call option with an exercise price above the current index level. The spread is a bull spread because the trader hopes to profit from a rise in the Index. The trade is a spread because it involves buying one option and selling a related option. What is the advantage of entering into a bull spread? Compared to buying the underlying asset itself, the bull spread with call options limits the trader’s risk, but the bull spread also limits the profit potential. In

it, it limits both the upside potential as well as the downside risk. The cost of the bull spread is the cost of the option, i.e., purchased, less the cost of the option, le, sold..

  1. Bear Spreads: Sell a Call and Buy Another: There are the a call and Buy Another: There are times when an investor thinks the market ng to fall over the next two months, however, in the  me next two months, however, in the event that the market does not like to limit his downside. One way he could do this is by entering into a spread. A spread trade strategy involves taking a position in two or more options of the same type, Less two or more calle two or more puts. A spread, i.e., designed to profit if the price goes down is called a bear spread.

In a bear spread, the strike price of the option purchased is greater than the strike price of the option sold. The buyer of a bear spread buys  with an exercise price above the current index level sells a call option with an exercise price below the current index level. The spread is a bear som because the trader hopes to profit from a fall in the index. The trade is a spread because it involves buying one option and selling a related option. What is the advantage of entering into a bear spread compared to buying the index itself? The bear spread with call options limits the traders risk, but also limits the profit potential. In short, it limits both the upside potential as well as the downside risk.

Ques.16. Explain the following terms:

  1. Box spread,
  2. Butterfly spread, 3. Straddle,
  3. Strangle.

Ans. 1. Box Spread: A box spread is a combination of bull spread with calls and bear spread with puts, at the same exercise price. The box spread will always pay the difference between the high and! low exercise price. However, the initial investment that is needed should not be greater than the final pay-off. In a perfect market, where the prices are correctly fixed based on consistent assumptions on! volatility and risk-free rates, there will be no scope to enter into a box spread at all. But when the market has differently interpreted assumptions for volatility and risk-free interest, the price can offer scope for a box spread.

  1. Butterfly Spread: A butterfly is an options strategy using multiple puts and/or calls speculating on future volatility without having to guess in which direction, the market will move. A long butterfly comprises three types of either puts or calls having the same expiration date but different exercise prices (strikes).

A long butterfly can also be created by selling a put and a call that are ATM and buying a put at the lowest strike and a call at the highest strike. Such a strategy is termed as iron butterfly

  1. Straddle: In finance, a straddle is an investment strategy that involves the purchase or sale of particular option derivatives that allow the holder to make profit on the basis of the magnitude of price movement in the underlying security without considering the direction of price movement.

Straddle is an appropriate strategy for an investor who expects a large move in the index but does not know that in which direction the move will be.

  1. Strangle: A strangle is an options strategy similar to a straddle, but with different strike prices on the call and put options. This is used to bias the profitability of the strategy towards one particular direction of price movement in the underlying, while still offering some or a reduced protection against a movement in another direction.

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