C) Option markets and contracts

2. C) Option markets and contracts

3. identify the basic elements and describe the characteristics of option contracts; • An option is a contract. • It gives one party (the holder of the option) the right to choose, during a specified period of time, to buy (or sell, respectively) a specified quantity of a specified asset (for instance a stock) at a given price. • The other contract party (the writer of the option) has the obligation to fulfill the holder's right.

4. Put Option Call Option Long- Buyer of Put- Holder Short- Seller of Put- Writer Long- Buyer of Put- Holder Short- Seller of Put- Writer

5. define European option, American option, money ness, payoff, intrinsic value, andtime value • American option: may be exercised at any time up to and including the contracts expiration date • European option: can be exercised only on the contract’s expiration period. • At expiration an American and an European on the same asset and the same strike price are equal

6. define European option, American option, money ness, payoff, intrinsic value, andtime value.. Contd .. • If 2 options are identical in all respects, except that one is American and the other is European, tha value of an American option will equal or exceed the value of European option

7. Options Terminologies. • In-the-money: • At-the money • Out of Money

9. Intrinsic Value of an Option.. • An option’s intrinsic value is the amount by which the option is in-the money. It is the amount that an option owner would receive if the option were exercised. • An option has a zero intrinsic value if it is it is at the money or out of money, regardless of whether it is a call or put

10. Intrinsic Value of an Option..contd • Lets look at the value of a call option at expiration. If the expiration date date price of the stock exceeds the strike price of the option. The call owner will exercise the option and receive S-X. if the price of the stock is less that the strike price, the call holder will let the option expire and get nothing.

11. Intrinsic Value of an Option..contd • The intrinsic value of the call option at expiration is the greater of (S-X) or 0. That is C= max(0, S-X)

12. Value Put Option pay off Strike Price of 50 Long Call 5 0 -5 Short Call Stock price at expiration X=50 X=55

13. Value Call Option pay off Strike Price of 50 Long put 10 0 -10 Short Put X=40 X=50 Stock price at expiration

14. Time Value • The time value of an option is the amount by which the option premium exceeds the intrinsic value and is sometimes called the speculative value of the option. Option value= intrinsic value+time value.

15. As discussed earlier, the intrinsic value of an option is the amount by which the option is in the money At any point during the life of an option its value will be typically greater than its intrinsic value. This is because there is some probability that the stock price will change in an amount that gives the option a positive pay off at expiration greater that the current (intrinsic) value. Recall that an option’s intrinsic (to a buyer) is the amount of payoff at expiration and is bounded by zero. When an option reaches expiration there is no time remaining and the time value is zero. For American options and most cases for European options the longer the time to expiration, the greater the time value and other things being equal, the greater the options premium

16. Identify different types of options • Financial Options • Options on futures • Commodity Options

17. Financial Options • Bond Options • Index Options*cash settled • Stock Options

18. Option on futures • Sometimes called futures options, give the holder the right to buy or sell a specified futures contract on or before a given date enter into a long side of a futures contract at a given futures price. Assume that you hold a call option on a bond future @ 98 % of the face value and at the expiration the future price of the bond is 99. By exercising the call, you can take a long position in the futures contract, and the account is immediately marked to market on the settlement price. Your account will be credited with an cash amount of 1% of the face value of the face value of the bond. • The seller of the exercised call will take a short position in the futures contract and the mark to market value of this position will generate the cash position deposited in your account a

19. Compare IRO & FRA. • IRO are similar to stock options except that the exercise price is an interest rate and the underlying asset is a reference rate • IRO are also similar to FRA because there is no delivery asset, instead they are settled in cash

20. Consider a long position in a LIBOR based Interest rate call option with a notional amount of $ 1000000 and a strike rate of 5%. • If at expiration libor is greater than 5% the option can be exercised and the owner will receive 1000000*(LIBOR-5%). • IF Libor is less than 5%, the option expires worthless

21. Interest rate cap and floor • An interest rate cap is a series of interest rate call option, having expiry dates that corresponds to the reset dates on the floating rate loan. Caps are often used to protect a floating rate borrower from an increase in the interest rates. Caps places a maximum limit on the interest rates on the floating rate • Caps pay when rates rise above the cap rate. In this regard, a cap can be viewed as a series of interest rate call options which strike equals to the cap rate. Each option in a cap is called a caplet.

22. Interest rate cap and floor • An interest rate floor is a series of interest rate put option, having expiry dates that corresponds to the reset dates on the floating rate loan. Floors are often used to protect a floating rate lender from an decline in the interest rates. Floors places a minimum limit on the interest rates on the floating rate • Floors pay when rates fall below the floor rate. In this regard, a floor can be viewed as a series of interest rate put options which strike equals to the floor rate. Each option in a floor is called a floor let

23. Example • In the event that LIBOR rises above 10%, the cap will make a payment to the cap buyer to offset any interest expenses in excess of an annual rate of 10%

24. Loan Rate Loan rate without caps or Floors Received by cap owner 10% 10% cap 5% floor 5% Received by floor owner 10% 5% LIBOR

25. Identify the minimum and maximum values of European and American Options Lower case letters are used to denote European style options

26. Lower bounds for Options (Call & Put) for both American and European options. • Theoretically no option will sell for less than its intrinsic value and no option can take a negative value. • This means that the lower bound for any any option is zero for both Americans and European options

27. Upper bounds for call Options (American and European ) • The maximum value of either an American or European call option at any time t is the time t share price of the underlying stock. This makes sense because no one would pay a price for a right to buy an asset that exceeds the assets value. It would be cheaper to simply buy the underlying stock • At time t=0, the upper boundary condition can be expressed respectively for American and European call option is American Option C0 <= S0 European Option C0 <= S0

28. Upper bounds for PUT Options (American and European ) • The price for an American put option cannot be more than its strike price. This is the exercise value in the event the underlying stock price goes below zero. However, since the European puts cannot be exercised prior to expiration, the maximum value is the PV of the exercise price discounted at the RFR.

29. Upper bounds for PUT Options (American and European ) • Even if the exercise price goes to zero and is expected to stay zero, the intrinsic value X, will not be received until expiration date. At time t=0, the upper boundary condition can be expressed for American and European option can be expressed as • P0<=X and p0 <=X/1+( RFR) ^ t

30. Option Strategies. • Basic Options Strategy: -Long on call -Short on call -Long on Put -Short on put • Spread Strategies -Bull spread.(Buy call-Sell call @ Higher Exercise Price)-Market view Bullish -Bear spread. (Buy call-Sell call @ Lower Exercise Price).-market view Bears

31. Option Strategies. • Straddle-market View Mixed(volatile) -Long Straddle -Short Straddle • Strangle -market View Mixed(Range bound) -Long Straddle -Short Straddle

32. Spread Strategy

33. Bull Spread

34. Spread Strategy

35. Bear Spread

36. Straddle-market View Mixed LONG Straddle

38. Short Straddle

44. INTRINSIC VALUE • For a call option:Intrinsic value = Price of the underlying - Exercise price • For a put option: Intrinsic value = Exercise price - Price of the underlying

45. FACTORS AFFECTING PREMIA • There are five major factors affecting the Option premium: • Price of Underlying • Exercise Price Time to Maturity • Volatility of the Underlying • And two less important factors: • Short-Term Interest Rates • Dividends

46. Intuition would tell us that the spot price of the underlying, exercise price, risk-free interest rate, volatility of the underlying, time to expiration and dividends on the underlying(stock or index) should affect the option price.

47. OPTION Pricing

48. Black and Scholes start by specifying a simple and well–known equation that models the way in which stock prices fluctuate. This equation called Geometric Brownian Motion, implies that stock returns will have a lognormal distribution, meaning that the logarithm of the stock’s return will follow the normal (bell shaped) distribution.

49. The Black-Scholes (1973) option pricing formula prices European put or call options on a stock that does not pay a dividend or make other distributions