摘要
为使股票模型和利率模型更贴近且反映金融市场实际情况,建立了股票价格遵循指数O-U(Ornstein-Uhlenback)过程模型的随机微分方程。由于假设利率是常数具有不合理性,此时假设利率不再是无风险利率,也会出现随机的变化。文章在随机利率服从Vasicek利率模型情况下,在风险中性的假设前提下,利用随机分析中Girsanov定理找到了O-U过程模型的唯一等价鞅测度,以期权定价的鞅方法及概率论的知识作为主要结果获得了欧式期权看涨及看跌的定价公式,为市场投资者理性投资分析提供指导和参考。
In order to make the stock model and interest rate model closely reflect to the real situation of the financial market,the paper constructed the stochastic differential equation of the stock price whose process was driven by the exponential O-U process.Because it is irrational if interest rate is constant,the interest rate is not risky any more,it always appears to be stochastic changes.In some case that the stochastic interest rate is obeyed the Vasicek interest rate model and under the hypothetical premise of risk-neutral,the unique equivalent martingale measure of O-U process model is found by means of Girsanov theorem from stochastic calculus and by way of the martingale method of pricing options and probability.From the research outcome,the pricing formula of European call option and put option are obtained.The research can imply the certain instruction significance to the market investors.
出处
《荆楚理工学院学报》
2011年第2期47-51,共5页
Journal of Jingchu University of Technology
