次分数布朗运动机制下的外汇期权定价模型

Pricing Currency Options in Sub-fractional Brownian Motion Regime

次分数布朗运动可较好地刻画标的资产价格波动长程相关性的特征.文章主要探究次分数机制下外汇期权的定价问题.运用Delta对冲方法,得到模型下外汇期权满足的偏微分方程定解问题.进一步给出外汇期权的定价公式及相关数值计算结果.结果表明,在相同参数下,外汇期权在次分数机制下的价格低于其在布朗运动机制下的价格.

Sub-fractional Brownian motion can better characterize long-range correlations of the underlying assets price well.This paper mainly studies the pricing of foreign exchange option under the sub-fractional regime.The partial differential equation which the foreign exchange option satisfied is obtained by using Del⁃ta hedging method.Moreover,the pricing formula for foreign exchange option and some relevant numerical re⁃sults are given.The results show that under the same parameters,the price of foreign exchange option under⁃sub-fractional regime is lower than that underthe Brownian motion regime.