次扩散过程驱动下的两值期权定价

Pricing of Binary Options in Sub-Diffusive Regime

期权定价是金融数学的重要问题之一,而两值期权是一种具有不连续收益的新型期权,其作为一种重要的新型期权使得资产收益更贴合投资者需求,为研究复杂期权提供了一种重要工具。在已有期权定价模型中,标的资产价格变化的随机驱动源通常为布朗运动和分数布朗运动,但它们无法刻画标的资产常值周期性的特征。为了解决这一问题,本文基于次扩散过程,对两值期权产品的定价展开研究,建立了次扩散机制下两值期权定价模型。运用Δ对冲技巧和Ito公式得到了两值期权在次扩散机制下所满足的偏微分方程,并给出了资产或无值看涨期权和现金或无值看涨期权的定价公式。

Option pricing is one of the important issues in financial mathematics.Binary option is a novel type of option with discontinuous returns.As an important new type of option,binary option makes asset returns more suitable for investors'needs,and provides an effective tool for studying complex options.In the present option pricing models,the random driving sources of the underlying asset’s price change are usually Brownian motion and fractional Brownian motion,which either cannot describe the constant cyclical characteristics of the underlying asset.Therefore,in order to solve this problem,we study the pricing of binary option products based on sub-diffusive process and establish a binary option pricing model under the sub-diffusive regime.The partial differential equation satisfied by the binary option under the sub-diffusive regime are obtained by using Delta hedging technique and Ito formula.And the pricing formulas of asset-or-nothing call options and cash-or-nothing call options are given.