带不对称跳的期权定价扩散模型的参数估计

The Parameter Estimation of Asymmetric Jump Diffusion Model for Optional Pricing

从期权价格变化的波动率微笑问题出发,对传统的Black-Scholes期权定价模型进行了改进.当股票或期权价格发生跳跃时,选取期权价格的上跳和下跳过程分别服从Pareto分布和Kumaraswamy分布,建立期权定价的不对称跳扩散模型.进一步地,对Pareto分布和Kumaraswamy分布的两种参数估计方法进行比较,通过模拟研究结果分析其差别,选出相对较优的参数估计方法,并给出合理解释.

In view of the volatility smile and the asymmetric jump of option price, the traditional Black Scholes option pricing models are improved. The Pareto distribution and Kumaraswamy distribution are adopted respectively to describe the plummets and spikes of option price. Furthermore, two parameter estimation methods of the Pareto distribution and Kumaraswamy distribution—maximum likelihood estimation and Bayes estimation are introduced. According to the computer simulation results, two estimation methods are compared to choose the better method.