基于不确定指数O-U过程带有浮动利率模型的亚式期权定价

Asian Option Pricing Formulas Based on the Uncertain Exponential Ornstein-Uhlenbeck Model with Floating Interest Rate

不确定金融是不确定理论在现代金融领域的一种应用,在解决金融问题中发挥着越来越重要的作用。而利率是一个重要的经济指标,经常受到一些不确定因素的影响,在研究期权定价时,有必要考虑浮动利率。本文提出了一种新的不确定指数Ornstein-Uhlenbeck过程模型,假设利率服从不确定均值回复过程,研究了期权定价问题,运用α-轨道方法,分别推导了亚式看涨期权和看跌期权定价公式。最后,设计了计算期权价格的数值算法,并给出数值算例。

Uncertain finance is an application of uncertainty theory in the field of modern finance and plays a more and more important role in solving the financial problems.As an important economic indicator,interest rate is always affected by some uncertain factors.It is necessary to consider the floating interest rate when we investigate the option pricing.This paper proposes a new uncertain exponential Ornstein–Uhlenbeck stock model with floating interest rate,where interest rate is assumed to be the uncertain mean-reverting model.Subsequently,the Asian call option pricing formulas and put option pricing formulas are derived via theα-path method.Besides,some numerical algorithms are designed to compute the prices of these options and some numerical examples are performed.