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Chapter 20

Chapter 20. Option Valuation and Strategies. Option Valuation and Strategies. Option valuation determines what an option is worth Option strategies means to use options as speculative or risk-management tools. Option Value. What determines line DE’s position?.

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Chapter 20

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  1. Chapter 20 Option Valuation and Strategies

  2. Option Valuation and Strategies • Option valuation • determines what an option is worth • Option strategies • means to use options as speculative or risk-management tools

  3. Option Value • What determines line DE’s position?

  4. Black / Scholes Option Valuation Model • Value of an option depends on • price of the stock • strike price • time to the option's expiration • variability of the stock’s return • rate of interest

  5. Black / Scholes Model in Equation Form • V0 = Ps x F(d1) - Pe/erT x F(d2)

  6. Black / Scholes Option Valuation Model • Except for the variability of a stock's return, all the variables are observable • The historical standard deviation of a stock's return is often used to measure the current variability of a stock's return

  7. The Anticipated Relationships (for calls) • Higher stock price - higher valuation • Lower strike price - higher valuation • Longer term - higher valuation • Increased variability - higher valuation • Higher interest rate - higher valuation

  8. Variability • Generally increased variability (increased risk) is associated with lower security valuationsBUT • More variability increases the likelihood the stock's price may rise • The higher stock price increases a call option's valuation

  9. Interest Rates • Generally higher interest rates are associated with lower security valuationsBUT • Higher interest rates reduce the present value of the call option's strike price. This reduction increases the option's valuation

  10. Black / Scholes • Black/Scholes uses a normal probability distribution • As the probability of an option being exercised rises, so does the valuation

  11. Black / Scholes

  12. Black / Scholes

  13. Put-Call Parity • The values of stocks, options, and debt instruments are interrelated • Put-call parity verifies the interrelationships

  14. Price of Stock • The price of a stock must equal • price of the call plus • present value of the strike price minus • price of the put

  15. Put-Call Parity Equation • Ps = Pc + Pe / (1 + i) - Pp • If the two sides are not equal • an opportunity for a risk-free arbitrage exists • If price of one of the four components changes, the price change is transferred to the remaining three

  16. Hedge Ratio • Determines the number of options necessary to offset a price movement in a stock • Is derived from the Black/Scholes valuation model

  17. Covered Put Strategy • Short the stock and sell the put • The opposite of the "covered call" • buy the stock and sell the call • Takes advantage of the declining time premium paid for the put

  18. Covered Put Strategy • Limited profit but unlimited potential loss

  19. Protective Call Strategy • Short the stock and buy the call • The opposite of the "protective put" • buy the stock and the put • Protects from the price of the stock rising

  20. Profit / Loss Profile for the Protective Call

  21. The Straddle • Buy a call and a put with the same strike price • Takes advantage of • major movements in the price of the stock • uncertainty concerning the direction of change in a stock’s price

  22. The Straddle • Buying a straddle generates profits only if the price of the stock moves sufficiently to cover the cost of the two options purchased

  23. The Straddle

  24. The Straddle • Writing a straddle is selling a call and a put with the same strike price • Is profitable if the price of the stock is stable

  25. The Straddle

  26. The Bull Spread • Requires two options with different strike prices and the same expiration date • To construct a bull spread using calls • buy the option with the lower strike price • sell the option with the higher strike price

  27. The Bear Spread • Requires two options with different strike prices and the same expiration date • To construct a bear spread using calls • sell the option with the lower strike price • buy the option with the higher strike price

  28. Bull and Bear Spreads • Bull and bear spreads have limited potential profits • Bull and bear spreads have limited potential for loss

  29. Bull and Bear Spreads • Profits and losses on bull and bear spreads are mirror images

  30. Bull and Bear Spreads

  31. The Butterfly Spread • Requires three options with • different strike prices and • the same expiration date • Buy the one each of the options with the extreme strike prices and sell two of the options with the middle strike price

  32. The Butterfly Spread • The process may be reversed: Sell one each of the options with the extreme strike prices and buy two of the options with the middle strike price

  33. The Butterfly Spread

  34. The Butterfly Spread • Profits and losses from the two butterfly spreads are mirror images • The butterfly spread has limited potential profits but limited potential for loss

  35. Collars • Used when an investor desires to lock-in a large gain • Sell a call at one strike price and • Buy a put with a lower strike price

  36. Collars • The cash inflow from the sale offsets the cost of the put • The put protects the investor from a decline in the price of the stock

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