Pricing and hedging path-dependent options under the CEV process
Pricing and hedging path-dependent options under the CEV process
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DOI：
10.1287/mnsc.47.7.949.9804
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发表时间：
2001-07-01
影响因子：
5.4
通讯作者：
Linetsky, V
中科院分区：
文献类型：
--
作者：
Davydov, D;Linetsky, V
路径相关期权的大部分工作都假设基础资产价格遵循具有恒定波动率的几何布朗运动。本文对资产价格过程使用了更一般的假设，该假设与实证观察结果提供了更好的拟合。我们使用所谓的恒定方差弹性（CEV）扩散模型，其中波动率是标的资产价格的函数。在此假设下，我们推导出了重要类型的路径相关期权价格的解析公式。我们证明，期权的价格，这取决于极值，如障碍和回望期权，可以更敏感的规范的基础价格过程比标准的看涨期权和看跌期权，并表明，金融机构，使用标准的几何布朗运动假设是暴露于显着的定价和对冲错误时，在处理路径依赖的选项。
Much of the work on path-dependent options assumes that the underlying asset price follows geometric Brownian motion with constant volatility This paper uses a more general assumption for the asset price process that provides a better fit to the empirical observations. We use the so-called constant elasticity of variance (CEV) diffusion model where the volatility is a function of the underlying asset price. We derive analytical formulae for the prices of important types of path-dependent options under this assumption. We demonstrate that the prices of options, which depend on extrema, such as barrier and lookback options, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.