随机波动率与跳组合情形的期权问题闭式解

Closed-Form Solution of the Option Problem under the Combination of a Stochastic Volatility Process and a Jump Process

围绕著名Black-Scholes模型的推广,当前学术界有两种途径:一是允许波动率为随机的;二是引入随机跳.实证表明,虽然随机波动率模型稍好,但二者效果都不太理想.为能更真实地反映资产价格变动的规律,本文首次引入对数正态随机波动率过程与一个复合Poisson过程组合的资产价格动态模型,并得到了该模型下欧式看涨期权定价的闭式解.

In order to generalize the Black-Scholes model, there are two ways in the literature so far. The first one assumes the volatility follows a stochastic process. The other one introduces jumps into the return process. However, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models faro somewhat better than jumps. As for this, here we propose an new model, where asset prices are given by the combination of a log-normal stochastic volatility process and an compound Poisson process. The closed-form solution to the valuation of European option has been derived.