基于一般随机波动跳扩散过程的几类多变量交换期权定价及创新研究

Pricing and Innovative Research on Multivariate Exchange Options Based on General Stochastic Volatility Jump-Diffusion Processes

摘要: 本文重点讨论了某种一般随机波动跳扩散过程下几类多变量交换期权的解析定价问题。首先，金融市场的状态转换特征，设计了具有体制转换特征的一般随机波动跳扩散模型用以描述资产价格的演变机制，主要刻画资产收益率间的联合波动和联合跳跃的综合特征。其次，为了解析定价的需要，构建所有相关随机因素的特征函数，并通过一系列的定理准备工作，最终获得特征函数的解析表达式。再次，运用风险中性定价原理，推导六类多变量交换期权的积分定价公式。最后，应用上述公式，构建了交叉KMV模型并进行金融市场风险分析。实验结果表明，本文所提供的理论能够有效地、稳定地解决多变量交换期权的定价问题及金融市场的风险分析问题。

Abstract: This paper mainly discusses the analytical pricing issues of several types of multivariate exchange options under a certain general stochastic volatility jump-diffusion process. Firstly, based on the state transition characteristics of the financial market, a general stochastic volatility jump-diffusion model with regime-switching features is designed to describe the evolution mechanism of asset prices, mainly depicting the combined characteristics of joint volatility and joint jumps among asset returns. Secondly, to meet the requirements of analytical pricing, the characteristic functions of all relevant stochastic factors are constructed, and through a series of preparatory theorems, the analytical expression of the characteristic function is finally obtained. Thirdly, by applying the risk-neutral pricing principle, the integral pricing formulas for six types of multivariate exchange options are derived. Finally, the cross-KMV model is constructed using the above formulas and applied to financial market risk analysis. The experimental results show that the theory provided in this paper can effectively and stably solve the pricing problems of multivariate exchange options and the risk analysis of financial markets.