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对执行价格的凹性
F是执行价格的减函数
分布相同，起始相同，期权价值相同
组合的期权价值小于期权组合的价值
期权价格是标的股票风险的非减函数
齐次性
对标的股票价格的凹性
contents: 红利保护的条件； 红利对非红利保护期权的影响； 执行价格变动的影响。 8.3 Effects of Dividends and Changing Exercise Price contents: 红利保护的条件； 红利对非红利保护期权的影响； 执行价格变动的影响。
Definition: （什么是红利保护期权。） 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.（保证期权价值不变。） 对投资与资本结构政策实施红利保护不太可能。这两者会改变股票的风险。
对B-S例子的反驳：对红利保护的定义不同（不重要。） 执行价格可变的情况。 提前执行只可能在红利支付前那一刻。 所以有红利支付的美式权证可以经调整的欧式权证，运用动态规划的基本思想回溯求解。
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