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Introduction to Financial Derivatives

Introduction to Financial Derivatives. Lecture #5 on option Jinho Bae May 27, 2008. Ch 8. Option pricing models. I. Value of an option Intrinsic value Time value Time value 1 Time value 2 II. Factors that affect the price of an option. I. Value of an option.

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Introduction to Financial Derivatives

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  1. Introduction to Financial Derivatives Lecture #5 on option Jinho Bae May 27, 2008

  2. Ch 8. Option pricing models I. Value of an option • Intrinsic value • Time value • Time value 1 • Time value 2 II. Factors that affect the price of an option

  3. I. Value of an option • Value of an option= Intrinsic value + Time value • Intrinsic value of an option • Call option max (S-X, 0) • Put option max (X-S, 0)

  4. I-2. Time value of an option • The value of an option arising from the time left to maturity • Time value = Option premium - Intrinsic value • Time value 1: Expected payoff from holding the option until maturity

  5. Time value 1 of a call option value Time value 1 X S Current spot price OTM ITM

  6. Time value 1 of a put option value Time value 1 X S ITM OTM

  7. 2) Time value 2 • Time value associated with cash flow arising from option writer’s selling or buying underlying asset of the option • Call (put) option writers buy (sell) underlying asset when they write the option • Why do they do so? • What is the cash flow?

  8. Time value 2 of a call option • Why do call option writers buy the asset when they write the option? • When a call option is exercised, call option writer is required to sell an underlying asset to option holder • In preparation for this, the writer buys the underlying asset

  9. Cash flow associated with the purchase of the asset • Option writer pays the asset price • He/she gives up interest that the money could earn until maturity • Why? • If he/she does not write the option, the writer need not pay the price • Thus, the interest is opportunity cost of writing option • Option writer adds the opportunity cost to the option price

  10. Size of the interest • Depends on the amount of the asset that is purchased • How many underlying assets should the writer buy? • The amount that is purchased depends on the probability that the option is exercised • If the probability is low, buy only a small portion of option positions • If the probability is high, buy a large portion of option positions • If the probability is 1, buy as many as option positions • What determines the probability? • The current underlying asset price S relative to the exercise price X • If S ≫ X (deep ITM), the probability is very high  very large interest • If S > X (shallow ITM), the probability is high  large interest • If S < X (shallow OTM), the probability is low  small interest • If S ≪X (deep OTM), the probability is very low  very small interest

  11. Time value 2 of a call option Value Time value 2 X S OTM ITM

  12. Time value1 and 2 of a call option Value Time value1 Time value2 X S OTM ITM

  13. Total time value of a call option value Time value X S OTM ITM

  14. Characteristics of time value of a call option • Not symmetric around X • Bigger when ITM than when OTM • Due to asymmetry of interest cost • Always non-zero

  15. Value of a call option (summary) value Time value Intrinsic value X S

  16. Time value 2 of a put option • When a put option is exercised, the option writer is required to buy the asset • In preparation for this, the writer short-sells the underlying asset when writing the option

  17. Option writer short-sells the underlying asset • The proceeds earn interest until maturity • If he/she did not write the option, the writer would not earn the interest • Option writer lowers the option price by the interest • Time value 2 of a put option is negative

  18. Size of the interest • Depends on the amount of the asset that is short-sold • The amount is determined by the probability of exercising a put option • The probability depends on S • If S≪X (deep ITM), very high probability • If S < X (shallow ITM), high probability • If S > X (shallow OTM), low probability • If S≫X (deep OTM), very low probability • The higher the probability, the larger portion of option positions the writer short-sells, and the larger the interest

  19. Time value 2 of a put option Value ITM OTM X S Time value2

  20. Time value1 and 2 of a put option value Timevalue1 Time value2 X S OTM ITM

  21. Total time value of a put option value Time value S X OTM ITM

  22. Characteristics of time value of a put option • Not symmetric around X • Bigger when OTM than when ITM • This is due to asymmetry in time value 2 • Total time value can become negative when time value 2 exceeds time value 1 at very deep ATM

  23. 3. Overall time value of a call option is slightly larger than that of a put option • For call options, interest is included in time value • For put options, interest is excluded from time value

  24. Value of a put option (summary) Value S X

  25. II. Factors that affect the price of an option • Underlying asset price S • Exercise price X • Time left to maturity • Variability of underlying asset price • Interest rate

  26. 1) Underlying asset price S Other things being equal, as S increases, • call option price rises • Put option price falls

  27. Underlying asset price and call option price Value S X

  28. KOSPI200 C 200806 220 S c 5/26/2008 230.43 12.40 5/27/2008 233.15 14.15

  29. Underlying asset price and put option price Value S X

  30. KOSPI200 P 200806 220 S p 5/26/2008 230.43 1.27 5/27/2008 233.15 0.85 (12:15 pm)

  31. 2) Exercise price X Other things being equal, as X increases, • Call option price decreases since its intrinsic value decreases • Put option price increases since its intrinsic value increases

  32. KOSPI200 C 200806 (as of 12:16 pm on 5/27/2008)

  33. KOSPI200 P 200806 (as of 12:16 pm on 5/27/2008)

  34. 3) Time to maturity Other things being equal, • The longer the time to maturity, the larger option prices get • As we get closer to maturity, option prices fall

  35. 4) Variability of underlying asset price S Other things being equal, as S get more variable, option becomes more expensive

  36. Variability and call option price Value High variability Low variability S X

  37. Variability and put option price Value High variability Low variability S X

  38. 5) Interest rate • interest rate is related to option price through time value 2 Other things being equal, as interest rate rises, • Interest cost rises  call option price rises • Interest earning rises  put option price falls

  39. interest rate is related to option price through underlying asset price S Other things being equal, as interest rate rises,  S falls  call option price falls, put option price rises

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