Total value adjustment for a stochastic volatility model. A comparison with the Black–Scholes model

作者：

Highlights：

• highlights

• The total value adjustment (XVA) under the Heston model is studied for European and American options.

• Linear and nonlinear partial differential equations have been deduced modelling the XVA.

• Several numerical methods and suitable boundary conditions are proposed in order to solve the obtained PDEs

• A comparison with the Black-Scholes model is made with the numerical results.

• Expected exposures for Heston and Black-Scholes models are also computed.

摘要

highlights•The total value adjustment (XVA) under the Heston model is studied for European and American options.•Linear and nonlinear partial differential equations have been deduced modelling the XVA.•Several numerical methods and suitable boundary conditions are proposed in order to solve the obtained PDEs•A comparison with the Black-Scholes model is made with the numerical results.•Expected exposures for Heston and Black-Scholes models are also computed.

论文关键词：(non)linear PDEs,Heston model,Expected exposure,Potential future exposure,Credit value adjustment,Finite element method

论文评审过程：Received 30 July 2019, Revised 10 February 2020, Accepted 21 June 2020, Available online 9 September 2020, Version of Record 9 September 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125489