A Jump Diffusion Model for Option Pricing
A Jump Diffusion Model for Option Pricing
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DOI：
10.2139/ssrn.242367
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发表时间：
2001-08
期刊：
影响因子：
--
通讯作者：
S. Kou
中科院分区：
文献类型：
--
作者：
S. Kou
布朗运动和正态分布在Black- Scholes期权定价框架中被广泛应用于资产收益模型。然而，许多实证调查中出现了两个难题：与正态分布相比，资产回报分布可能具有更高的峰值和两个（不对称）更重的尾部的细峰特征，以及期权市场中称为“波动率微笑”的实证现象。为了兼顾这两方面，在期权定价的现实性和可追溯性之间取得平衡，本文提出了一种双指数跳跃-扩散模型。特别是，该模型足够简单，可以为各种期权定价问题提供分析解决方案，包括看涨期权和看跌期权、利率衍生品和路径依赖期权。均衡分析和模型的心理学解释也被提出。
Brownian motion and normal distribution have been widely used in the Black--Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called "volatility smile" in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jump-diffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of option-pricing problems, including call and put options, interest rate derivatives, and path-dependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.