随机波动率下永久美式障碍期权的渐近式

The Asymptotic Formula of the Perpetual American Barrier Option Under Stochastic Volatility

研究波动率服从快速均值回复Ornstein-Unlenbeck(O-U)过程的永久美式障碍期权的定价问题.考虑永久美式向下敲出看涨期权,该期权的定价问题可归结于求解自由边界问题.使用扰动法,把期权价格以及最优执行价格按均值回复时间长度的幂进行展开,通过求解Poisson方程组,得到期权和最优执行价格的渐近公式.

This study considers a stochastic volatility model for pricing perpetual American harrier options where the volatility is driven by a fast mean reversion Ornstein-Unlenheck （O-U） process.It takes the case of the perpetual down-and-out call option for example, pricing problem of which can be formulated as a free boundary problem.Using the perturbation method, we first expand the price and the optimal exercise price of this option in the power of the length of mean reversion time.Then,by solving a set of Poisson equations, two asymptotic formulae are derived for this option price and the optimal exercise price, respectively.