Chp.8 Theory of Rational Option Pricing

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1 Chp.8 Theory of Rational Option Pricing
Kangchaofeng

2 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.

3 8.2 Restrictions on Rational Option Pricing

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5 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.

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12 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.

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14 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.

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16 F对执行价格的凹性

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18 F是执行价格的减函数

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22 分布相同，起始相同，期权价值相同

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24 组合的期权价值小于期权组合的价值

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29 期权价格是标的股票风险的非减函数

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31 齐次性

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33 对标的股票价格的凹性

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35 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。

36 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。

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43 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。

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46 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.

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49 8.4 Restrictions on Rational Put Option Pricing

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59 8.5 Rational option Pricing along Black-Scholes Lines

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61 8.6 An Alternative Derivation of the Black-Scholes Model

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76 8.7 Extension of the Model to include Dividend Payments and Exercise Price Changes

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83 8.8 Valuing an American Put Option

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86 8.9 Valuing the “Down-and-out” Call Option

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91 8.10 Valuing a Callable Warrant

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