具有分数O-U过程的永久美式看跌期权的定价

该文研究具有分数Ornstein-Uhlenbeck过程的永久美式看跌期权的定价问题.首先, 利用分析金融衍生品定价的delta对冲方法和无套利原理, 遵循标准的讨论步骤, 建立了标的资产价格服从分数Ornstein-Uhlenbeck过程的欧式看涨期权和看跌期权的定价公式.然后, 通过求解一个自由边界问题, 对标的资产价格服从分数Ornstein-Uhlenbeck过程的永久美式看跌期权的定价以及实施该期权时的临界标的资产价格给出了显式解.

Pricing of Perpetual American Put with Fractional O-U Process

This paper studies the price of perpetual American put with fractional Ornstein-Uhlenbeck process. Using the basic building blocks of derivatives theory: delta hedging and no arbitrage principle, and following standard arguments, the authors first establish the pricing formulae for European calls and puts with fractional Ornstein-Uhlenbeck process, then the closed-form solutions for pricing of perpetual American put and the critical asset price when the underlying asset's price follows fractional Ornstein-Uhlenbeck process are obtained by solving a free boundary value problem.