常方差弹性系数模型下波动率指数期权定价

Pricing Volatility Index Option in Constant Elasticity of Variance Model

摘要:

作为对冲市场波动率变动风险的波动率指数期权，其定价问题一直受到广泛的关注.为了对其进行定价，首先构建服从常方差弹性系数模型的指数价格柳树，然后根据指数价格柳树确定柳树节点上相应波动率指数的值从而得到波动率指数柳树，最后在波动率指数柳树上运用倒向递归的方法得到波动率指数期权的价格.所给出柳树法定价波动率指数期权的方法，其结果随着柳树空间节点数的增加快速逼近嵌套蒙特卡罗模拟的结果，当柳树空间节点数超过200时，柳树法给出的结果具有相当高的精度.

Abstract:

As one of the most important tools to manage the risk of volatility, a lot of attention has been paid to volatility index options. In order to price these options, a willow tree of underlying index was built in the constant elasticity of variance model. Then, the value of volatility index at each node in the willow tree of underlying index was determined. Next, the willow tree of volatility index was used to price volatility index options by backward induction. Finally, an efficient way to price volatility index options was proposed. Numerical results show that the pricing results given by the willow tree are consistent with the results obtained from nested Monte Carlo simulation when the number of nodes on each time period in the willow tree is bigger than 200.