趋势与波动相关下的期权定价模型

唐毅南
复旦大学新政治经济学中心
Ynan.tang@gmail.com

陈平
复旦大学 新政治经济学中心, 北京大学 国家发展研究院

2010 年3 月26 日被《金融评论》接受

摘要：趋势与波动相互作用造成的相关性，是金融市场复杂性的根源。我们引入群
体动力学来统一描述平稳市场下的期权定价和金融危机。为此保留资产定价的无
套利组合机制，但放弃无风险利率（也即不变趋势）的假设，因为金融危机意味
着趋势的瓦解。我们用改进的HP 滤波器来识别变化的趋势，得到一般期权定价
模型，模型的解包含多重频率。金融衍生品市场崩溃的条件可以理解为危机心理
造成的趋势瓦解。Black-Scholes（BS）模型可以视为一般期权模型的一个特例。

关键词：趋势波动相关性，，期权定价，HP 滤波器

JEL 分类：C51, D53, G01

Option Pricing with Interactive Trend and Volatility

Abstract：Financial complexity is rooted in interaction between trend and volatility in option pricing. Population dynamics is introduced for developing a general model both for normal option market as well as financial crisis. The arbitrage portfolio can be preserved for option pricing. Therefore, the risk free interest rate is no longer valid, since financial crisis implies a trend collapse. The Hodrick-Prescott (HP) filter can be modified to separate trend from cycle series.The general model of option pricing can be solved with multiple frequencies.The condition of market collapse can be understood by trend collapse under crisis expectation. The Black-Scholes (BS) model can be obtained as a special case of the general model of option pricing.

Key Words: trend-volatility interaction, option pricing, HP filter, market crash

JELCS: C51, D53, G01

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