Exchange Option Pricing under the Hybrid Exponential Jump Diffusion Model
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摘要: 本文主要研究了在随机利率、随机波动率以及服从混合指数跳扩散模型下交换期权的定价问题.考虑到近几年市场上出现了负利率的情况,本文假设随机利率服从Hull-White (HW)模型,并在Heston波动率模型的基础上加入了混合指数跳,建立了混合指数跳扩散的Heston-HW (简记为MEJHeston-HW)模型.首先,采用测度变换的思路,通过傅里叶变换的方法推导出了交换期权的定价公式；然后,基于快速傅里叶算法得到了期权价值的数值解;最后,着重分析了随机波动率中的波动项、相关系数及跳跃强度对期权的价值影响.在数值模拟中,本文MEJ-Heston-HW模型与双指数跳HestonHW (简记为DEJ-Heston-HW)模型及Black-Scholes模型相比,本文的模型能更好地刻画金融资产价格的变动,因此本文得到的MEJ-Heston-HW模型下交换期权定价公式更符合金融市场规律,所得结果推广了已有的关于交换期权定价的相关结论.Abstract: This paper deals with the pricing of exchange options under the stochastic interest rate, stochastic volatility and mixed exponential jump diffusion model. On the basis of Heston volatility model, random interest rate and mixed index jump diffusion are introduced, and considering the negative interest rate in the market in recent years, this paper assumes that the interest rate model satisfies the Hull-White process (H-W), and establishes the mixed index jump Heston-HW (MEJ-Heston-HW) model. By using the idea of measure transformation, deduced the pricing formula of exchange options by Fourier transform method. Finally, based on the fast Fourier algorithm, the numerical solution of option value is obtained, and the influences of fluctuation term, correlation coeffcient and jump intensity in random volatility on option value are emphatically analyzed. Compared with the double exponential jump Heston-HW model (DEJ-Heston-HW) and Black-Scholes model, the MEJ-Heston-HW model can better describe the price changes of financial assets in numerical simulation. Therefore, the exchange option pricing formula under the MEJ-Heston-HW model is more consistent with the law of financial market, and the obtained results extend the existing conclusions on exchange option pricing.
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