基于神经随机微分方程的期权定价

Option Pricing Based on Neural Stochastic Differential Equations

首先,基于Black-Scholes股票价格模型,通过将资产回报率和波动率分别参数化为漂移网络和扩散网络,建立神经随机微分方程(NSDE)模型;其次,在实证分析中以标的资产为单只股票的期权作为研究对象,采用真实的股票数据进行网络训练和测试,实验结果表明,NSDE模型能克服Black-Scholes模型常数性假设的缺陷;最后,对于期权标的资产价格不可观测的情况,提出可以将任意一个目标期权的价格和一个已知期权的价格约束在其风险中性等价鞅测度的Wasserstein距离内,并在理论上证明该方法.

Firstly,based on the Black-Scholes stock price model,the neural stochastic differential equation(NSDE)model was established by parameterizing the asset return rate and volatility as a drift network and a diffusion network,respectively.Secondly,in the empirical analysis,the underlying asset as a single stock option was used as the research object,and real stock data was used for the network training and testing.The experimental results show that the NSDE model can overcome the defects of the constant assumption of the Black-Scholes model.Finally,for the case where the price of the underlying asset of the option was unobservable,we proposed that the price of any target option and the price of a known option could be constrained within the Wasserstein distance of their risk-neutral equivalent martingale measure,and theoretically proved the method.