分析对比不同波动率模型下的期权定价

Analysis and Comarision of the Option Pricing under Different Volatility

对理想市场模型下Black-Scholes期权定价公式的修正有很多文章,特别是Harrison and Kreps提出鞅方法定价后,出现了多种随机波动率下的定价模型。基于不完备的随机波动率模型,本文给出了不同著名鞅测度下定价的大小顺序。主要证明了期权价格随着风险市价的变化而减小,风险参数决定定价测度的选取,把此定理应用于最小鞅测度和q优测度下的定价。这在复杂的定价过程是很有意义的。

There are many methods about option pricing based on Black— Scholes model. There are many model about volatility,especially after Harrison and Kreps. This paper orders option prices under different well known martingale measures in an incomplete stochastic volatility model. The central result is a comparison theorem which proves option prices are decreasing in the market price of volatility risk, the parameter governing the choice of pricing measure. The theorem is applied to order option prices under the minimal martingale and q—optimal measures.