基于GBM模型的价差期权定价方法

Spread Options Pricing Methods Based on Geometric Brownian Motion Model

假定交易不连续,基于历史信息、风险偏好中性和几何布朗运动,文中主要从价差期权实值执行边界的不同情况出发,以定理的形式给出了价差期权和数字价差期权价格公式的优化方法,并确立了价差期权价格公式的解析近似解的恰当形式。同时,还对实值执行边界的单调性和凹凸性给出了性质定理,这在一定程度上方便了价差期权和数字价差期权的定价公式研究。

Option pricing plays an important role in financial mathematics research. Spread option is application and popularization of options. Assumes transactions are not continuous,based on historical information and risk-neutral preference and the Geometric Brownian motion as a reference model and taking different exercise boundaries in the money into consideration,the pricing optimization methods for spread option and digital spread option are introduced. Finally,the appropriate and closed-form formula for spread option and digital spread option is established.Furthermore,the monotonicity and convexity theorems of exercise boundary in the money is given,which facilitates the spread option and digital spread option pricing formula to a certain extent.