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Chapters 14/15 – Part 1 Options: Basic Concepts

Options Call Options Put Options Selling Options Reading The Wall Street Journal Combinations of Options Valuing Options An Option‑Pricing Formula Investment in Real Projects and Options Summary and Conclusions. Chapters 14/15 – Part 1 Options: Basic Concepts.

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Chapters 14/15 – Part 1 Options: Basic Concepts

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  1. Options Call Options Put Options Selling Options Reading The Wall Street Journal Combinations of Options Valuing Options An Option‑Pricing Formula Investment in Real Projects and Options Summary and Conclusions Chapters 14/15 – Part 1Options: Basic Concepts

  2. Options Contracts: Preliminaries • Option Definition. • Calls versus Puts • Call options • Put options. • Exercising the Option • Strike Price or Exercise Price • Expiration Date • European versus American options

  3. Options Contracts: Preliminaries Option Premium Intrinsic Value Speculative Value + = • Intrinsic Value • Speculative Value

  4. Value of an Option at Expiration Impact of leverage… Stock price is $50. Buy 100 shares Call strike is $50, price is $10. Buy 1 contract. Put strike is $50, price is $10. Buy 1 contract. ===================== C = S – E P = E - S

  5. Call Option Payoffs 60 40 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Buy a call Write a call

  6. 60 40 Buy a put 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 Write a put -40 -60 Put Option Payoffs

  7. Call Option Payoffs 60 40 Buy a call 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Exercise price = $50

  8. Call Option Payoffs 60 40 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Write a call Exercise price = $50

  9. Call Option Profits 60 40 20 0 0 10 20 30 40 50 60 70 80 90 100 Option profits ($) Stock price ($) -20 -40 -60 Buy a call Write a call Exercise price = $50; option premium = $10

  10. Put Option Payoffs 60 40 Buy a put 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Exercise price = $50

  11. Put Option Payoffs 60 40 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 write a put -60 Exercise price = $50

  12. Put Option Profits 60 Option profits ($) 40 20 Write a put 10 0 0 10 20 30 40 50 60 70 80 90 100 -10 Buy a put Stock price ($) -20 -40 -60 Exercise price = $50; option premium = $10

  13. The seller (or writer) of an option has an obligation. The purchaser of an option has an option. Selling Options – Writing Options 60 60 40 Option profits ($) 40 Buy a call 20 20 Write a put 0 0 10 20 30 40 50 60 70 80 90 100 Option profits ($) 10 0 Stock price ($) 0 10 20 30 40 50 60 70 80 90 100 -20 -10 Buy a put Stock price ($) -20 -40 Write a call -40 -60 -60

  14. Call Option Payoffs at Expiration (Δ exercise) E=0 60 E=50 50 40 30 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 20 10 0 Buy a call Stock price ($)

  15. Option Pricing Bounds at Expiration • Upper bounds • Call Options • Put Options • Lower Bounds • Call option intrinsic value • = max [0, S - E] • Put option intrinsic value • = max [0, E - S] • In-the-money / Out-of-the-money • Time premium/time decay • At expiration, an American call option is worth the same as a European option with the same characteristics.

  16. Reading The Wall Street Journal

  17. The last section concerned itself with the value of an option at expiration. This section considers the value of an option prior to the expiration date. Valuing Options

  18. Option Value Determinants Call Put • Exercise price • Stock price • Interest rate • Volatility in the stock price • Expiration date The value of a call option C0 must fall within max (S0 – E, 0) <C0<S0. The precise position will depend on these factors.

  19. Varying Option Input Values • Stock price: • Call: as stock price increases call option price increases • Put: as stock price increases put option price decreases • Strike price: • Call: as strike price increases call option price decreases • Put: as strike price increases put option price increases

  20. Varying Option Input Values • Time until expiration: • Call & Put: as time to expiration increases call and put option price increase • Volatility: • Call & Put: as volatility increases call & put value increase • Risk-free rate: • Call: as the risk-free rate increases call option price increases • Put: as the risk-free rate increases put option price decreases

  21. Option Value Determinants Call Put • Exercise price – + • Stock price + – • Interest rate + – • Volatility in the stock price + + • Expiration date + + The value of a call option C0 must fall within max (S0 – E, 0) <C0<S0. The precise position will depend on these factors.

  22. Market Value, Time Value and Intrinsic Value for an American Call The value of a call option C0 must fall within max (S0 – E, 0) <C0<S0. CaT> Max[ST - E, 0] Profit ST ST - E Market Value Time value Intrinsic value ST E In-the-money loss Out-of-the-money

  23. Puts and calls can serve as the building blocks for more complex option contracts. If you understand this, you can become a financial engineer, tailoring the risk-return profile to meet your client’s needs. Combinations of Options

  24. Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiration Value at expiration Protective Put strategy has downside protection and upside potential $50 Buy the stock Buy a put with an exercise price of $50 $0 Value of stock at expiration $50

  25. Protective Put Strategy Profits Value at expiration Buy the stock at $40 $40 Protective Put strategy has downside protection and upside potential $0 Buy a put with exercise price of $50 for $10 $40 $50 -$40 Value of stock at expiration

  26. Covered Call Strategy Value at expiration Buy the stock at $40 $40 Coveredcall $10 $0 Value of stock at expiration $30 $40 $50 Sell a call with exercise price of $50 for $10 -$30 -$40

  27. Long Straddle: Buy a Call and a Put Value at expiration Buy a call with an exercise price of $50 for $10 $40 $30 $0 -$10 Buy a put with an exercise price of $50 for $10 -$20 $30 $40 $50 $60 $70 Value of stock at expiration A Long Straddle only makes money if the stock price moves $20 away from $50.

  28. Short Straddle: Sell a Call and a Put Value at expiration A Short Straddle only loses money if the stock price moves $20 away from $50. $20 Sell a put with exercise price of $50 for $10 $10 $0 Value of stock at expiration $30 $40 $50 $60 $70 -$30 Sell a call with an exercise price of $50 for $10 -$40

  29. Put-Call Parity C = Call option price P = Put option price S = Current stock price E = Option strike price r = Risk-free rate T = Time until option expiration Buy the stock, buy a put, and write a call; the sum of which equals the strike price discounted at the risk-free rate

  30. Put-Call ParityBuy Stock & Buy Put Combination: Long Stock & Long Put Position Value Long Stock Long Put Share Price

  31. Put-Call ParityBuy Call & Buy Zero Coupon Risk-Free Bond @ Exercise Price Combination: Long Stock & Long Bond Position Value Long Call Share Price Long Bond

  32. Put-Call Parity Combination: Long Stock & Long Bond Long Stock Combination: Long Stock & Long Put Position Value Long Bond Position Value Long Call Long Put Share Price Share Price In market equilibrium, it must be the case that option prices are set such that: Otherwise, riskless portfolios with positive payoffs exist.

  33. The Black-Scholes Model Value of a stock option is a function of 6 input factors: 1. Current price of underlying stock. 2. Strike price specified in the option contract. 3. Risk-free interest rate over the life of the contract. 4. Time remaining until the option contract expires. 5. Price volatility of the underlying stock. The price of a call option equals:

  34. Black-Scholes Model Where the inputs are: S = Current stock price E = Option strike price r = Risk-free interest rate T = Time remaining until option expiration  = Sigma, representing stock price volatility, standard deviation

  35. Black-Scholes Model Where d1 and d2 equal:

  36. Black-Scholes Models Remembering put-call parity, the value of a put, given the value of a call equals: Also, remember at expiration:

  37. The Black-Scholes Model Find the value of a six-month call option on the Microsoft with an exercise price of $150 The current value of a share of Microsoft is $160 The interest rate available in the U.S. is r = 5%. The option maturity is 6 months (half of a year). The standard deviation of the underlying asset is 30% per annum. Before we start, note that the intrinsicvalue of the option is $10—our answer must be at least that amount.

  38. The Black-Scholes Model Assume S = $160, X = $150, T = 6 months, r = 5%, and  = 30%, calculate the value of a call. First calculate d1 and d2 Then d2,

  39. The Black-Scholes Model N(d1) = N(0.52815) = 0.7013 N(d2) = N(0.31602) = 0.62401

  40. Another Black-Scholes Example Assume S = $50, X = $45, T = 6 months, r = 10%, and  = 28%, calculate the value of a call and a put. From a standard normal probability table, look up N(d1) = 0.812 and N(d2) = 0.754 (or use Excel’s “normsdist” function)

  41. Real Options • Real estate developer buys 70 acres in a rural area. He plans on building a subdivision when the population from the city expands this direction. If growth is less than anticipated, the developer thinks he can sell the land to a country club to build a golf course on the property. • The development option is a ______ option. • The golf course option is a _______ option. • How would these real options change the standard NPV analysis?

  42. Collar: Buy a Put, Buy the Stock, Sell the Call Value at expiration Buy the stock at $80 Collar $49.33 $42.11 $2.76 Value of stock at expiration $0 $0.67 -$27.91 $120 $80 $50 Sell a call with exercise price of $120 for $2.76 Buy a put with exercise price of $50 for $0.67 -$80 NTS

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