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CONTINGENT CLAIMS

CONTINGENT CLAIMS. Any risky security has a payoff that is contingent on the “state of the world” e.g., equity and debt in our asset substitution and underinvestment problem examples Some securities make a payoff in a range of states or in one state, but zero otherwise

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CONTINGENT CLAIMS

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  1. CONTINGENT CLAIMS • Any risky security has a payoff that is contingent on the “state of the world” • e.g., equity and debt in our asset substitution and underinvestment problem examples • Some securities make a payoff in a range of states or in one state, but zero otherwise • e.g., lottery tickets, life insurance, my World Series tickets, options

  2. OPTION: A Contingent Claim

  3. CALL OPTION PAYOFF

  4. PUT OPTION PAYOFF

  5. PROPERTIES OF CALL OPTION PRICES

  6. IMPLICATIONS FOR CALL OPTION PRICES (nondividend-paying stocks) • The price of a European call option is at least the maximum of zero or the stock price minus the present value of the exercise price • An American call option will never be exercised early • American call option must have same value as equivalent European call option

  7. OPTION TIME PREMIUM:The Value of Waiting

  8. TIME PREMIUM CHARACTERISTICS • Since the payoff on an option is asymmetric, the ability to wait is valuable: • Option time premium is generally positive • Time premium decreases as an option becomes further in-the-money or out-of-the-money • Time premium is greatest when the option is exactly at the money

  9. OPTIONS AND RISK • What happens if risk of underlying asset increases? • Greater chance of a larger payoff • Downside payoffs are limited to zero • Implication: Option values increase with risk of underlying asset

  10. PUT-CALL PARITY(nondividend-paying stocks) Buy stock, buy put, sell call (option exercise price = X) Stock PriceCall Exer?Put Exer?Wealth S > X yes no X S < X no yes X S = X ? ? X  S0 + P0 - C0 = X/(1+rf)T

  11. Explicit Traded options Executive stock options Call provisions on bonds Convertible bonds Warrants Hidden Capital budgeting: (postponement, abandonment) Tax timing Common stock and risky debt OPTIONS ARE EVERYWHERE

  12. OPTION ELEMENTS OF EQUITY AND RISKY DEBT • Equity is like a call option on firm assets • Equityholders have “sold” assets to bondholders • By paying off the debt obligation (exercise price) equityholders can buy back assets • Risky debt contains an embedded put • Equityholders can put the assets to the bondholders and cancel bondholders’ claim

  13. MARKET VALUE BALANCE SHEET

  14. SIMPLE CASE: TWO POSSIBLE FUTURE STATES OF THE WORLD • Stock price now is 100/1.05 = 95.24 • Stock pays no dividend • Next year, stock price goes up ( by factor u =1.68) to 160 or down (by factor d =.63) to 60

  15. PRICING A EUROPEAN CALL OPTION • Suppose current stock price is $95.24, and we know that, one year from now, stock price will be either $60 or $160 • Consider two investment strategies: 1. Buy ten call options on stock with exercise price of $150. Cost = ? 2. Buy one share of stock and borrow 60/1.05 at 5% int. rate. Total cost = 95.24 - 57.14 = 38.1

  16. PRICING A EUROPEAN CALL OPTION Payoff from two strategies after one year: Strategy If S = 60 If S = 160 1 0 10x10 = 100 2 60 - 60 = 0 160 - 60 = 100 • Strategy 2 is a replicating strategy • Since both strategies have the same payoff, they must have the same cost • Value of call = $38.1/10 = 3.81

  17. BLACK-SCHOLES MODEL • C = call price • S = stock price • X = exercise price • rf = risk-free rate • T = time to expiration •  = std. dev. stock price changes • N( ) = cumulative std. Normal probabilities

  18. PUT OPTION PRICING • We can use put-call parity to derive a Black-Scholes put option pricing model

  19. IMPORTANT ASSUMPTIONS • Nondividend-paying stock • Constant interest rate • Stochastic process governing stock price movements stays constant

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