Chp.8 Theory of Rational Option Pricing Kangchaofeng Kcfxm@163.com

8.1 Why? Option is a particularly simple type of contingent-claim asset, so a theory of option pricing may leading to general theory of contingent-claims pricing.

8.2 Restrictions on Rational Option Pricing

Dominant : Security(portfolio) A is dominant over security (portfolio) B if, on some known date in the future, the return on A will exceed the return on B for some possible states of the world. Assumption 1: A necessary condition for rational option pricing theory is that the option be priced such that it is neither a dominant nor a dominated security.

Theorem 8.2 If the hypothesized conditions for Theorem 8.1 hold, an American warrant will never be exercised prior to expiration, and hence it has the same value as a European warrant.

Theorem 8.3 If the hypothesized conditions for Theorem 8.1 hold, the value of a perpetual warrant must equal the value of the common stock.

F

F

8.3 Effects of Dividends and Changing Exercise Price contents:

Definition: An option is said to be payout protected if, for a fixed investment policy and fixed capital structure, the value of the option is invariant to the choice of payout policy.

B-S

Corollary 8.11b If there is a finite number of changes in the exercise price of payout-protected perpetual warrant, then it will not be exercised and its price will equal the common stock price.

8.4 Restrictions on Rational Put Option Pricing

8.5 Rational option Pricing along Black-Scholes Lines

8.6 An Alternative Derivation of the Black-Scholes Model

8.7 Extension of the Model to include Dividend Payments and Exercise Price Changes

8.8 Valuing an American Put Option

8.9 Valuing the Down-and-out Call Option

8.10 Valuing a Callable Warrant