有限状态多期模型下的最小熵等价鞅测度及其应用

Minimal Entropy Martingale Measure for a Finite States Multi-Period Model and Its Application

采用有限状态多期模型描述股票价格变动过程,导出了有红利支付情形下的最小熵等价鞅测度,给出了股票价格变动趋势的风险中性预期与红利率和无风险利率之间相对大小的关系,从理论上证明了无风险利率大于股票红利率时,市场将呈现出一种向上的风险中性趋势;无风险利率小于股票红利率时,市场将呈现出一种向下的风险中性趋势;无风险利率等于红利率时,股票价格将围绕初始价格上下波动而没有明显的风险中性趋势.

A multi-period model was used to describe the dynamic of stock price, and the minimal entropy martingale measure was deduced for this model. The relationship between the relative magnitude of dividends rate and riskless interest rate and the expectation of the risk neural market was investigated. It is proved that there is a upward expectation when the riskless interest rate is larger than the dividends rate; there is a downward expectation when the riskless interest rate is smaller than the dividends rate; and there is no obvious tendency and the price is expected to move around the original price when the two rates are equal.