Option Pricing Under a Mixed-Exponential Jump Diffusion Model
提出资产价格跳跃大小服从混合指数分布的跳跃扩散模型，该模型能近似任意分布，并给出路径依赖期权的拉普拉斯变换解析解，数值实验表明公式易实现且准确。
This paper aims to extend the analytical tractability of the Black–Scholes model to alternative models with arbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixed-exponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and double-exponential jump diffusion models, because the mixed-exponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavy-tailed distributions. The mixed-exponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for path-dependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a high-order integro-differential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day. This paper was accepted by Michael Fu, stochastic models and simulation.