In this chapter, we turn our attention to option valuation issues. To understand most option valuation models requires considerable mathematical and statistical background. Still, many of the ideas and insights of these models can be demonstrated in simple examples, and we will concentrate on these. | Chapter 21 Option Valuation Intrinsic value - profit that could be made if the option was immediately exercised. Call: stock price - exercise price Put: exercise price - stock price Time value - the difference between the option price and the intrinsic value. Option Values Time Value of Options: Call Option value X Stock Price Value of Call Intrinsic Value Time value Factor Effect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expiration increases Interest rate increases Dividend Rate decreases Factors Influencing Option Values: Calls Restrictions on Option Value: Call Value cannot be negative Value cannot exceed the stock value Value of the call must be greater than the value of levered equity C > S0 - ( X + D ) / ( 1 + Rf )T C > S0 - PV ( X ) - PV ( D ) Allowable Range for Call Call Value S0 PV (X) + PV (D) Upper bound = S0 Lower Bound = S0 - PV (X) - PV (D) 100 200 50 Stock Price C 75 0 Call Option Value X = 125 Binomial Option . | Chapter 21 Option Valuation Intrinsic value - profit that could be made if the option was immediately exercised. Call: stock price - exercise price Put: exercise price - stock price Time value - the difference between the option price and the intrinsic value. Option Values Time Value of Options: Call Option value X Stock Price Value of Call Intrinsic Value Time value Factor Effect on value Stock price increases Exercise price decreases Volatility of stock price increases Time to expiration increases Interest rate increases Dividend Rate decreases Factors Influencing Option Values: Calls Restrictions on Option Value: Call Value cannot be negative Value cannot exceed the stock value Value of the call must be greater than the value of levered equity C > S0 - ( X + D ) / ( 1 + Rf )T C > S0 - PV ( X ) - PV ( D ) Allowable Range for Call Call Value S0 PV (X) + PV (D) Upper bound = S0 Lower Bound = S0 - PV (X) - PV (D) 100 200 50 Stock Price C 75 0 Call Option Value X = 125 Binomial Option Pricing: Text Example Alternative Portfolio Buy 1 share of stock at $100 Borrow $ (8% Rate) Net outlay $ Payoff Value of Stock 50 200 Repay loan - 50 -50 Net Payoff 0 150 150 0 Payoff Structure is exactly 2 times the Call Binomial Option Pricing: Text Example 150 0 C 75 0 2C = $ C = $ Binomial Option Pricing: Text Example Alternative Portfolio - one share of stock and 2 calls written (X = 125) Portfolio is perfectly hedged Stock Value 50 200 Call Obligation 0 -150 Net payoff 50 50 Hence 100 - 2C = or C = Replication of Payoffs and Option Values Generalizing the Two-State Approach Assume that we can break the year into two six-month segments. In each six-month segment the stock could increase by 10% or decrease by 5%. Assume the stock is initially selling at 100. Possible outcomes: Increase by 10% twice Decrease by 5% twice Increase once and decrease once (2 paths). Generalizing the Two-State Approach 100 110 121 95 Assume that we
