# A note on a PDE approach to option pricing under xVA

@article{Baustian2021ANO, title={A note on a PDE approach to option pricing under xVA}, author={Falko Baustian and Martin Fencl and Jan Posp{\'i}sil and Vladim{\'i}r Sv{\'i}gler}, journal={ArXiv}, year={2021}, volume={abs/2105.00051} }

In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different value adjustments denoted generally as xVA are nowadays added to the risk-free financial derivative values and the PDE approach allows their easy incorporation. The aim of this paper is to show how to solve the PDE analytically in the Black-Scholes setting to get new semi-closed formulas that we compare to the widely used Monte-Carlo simulations and to the numerical solutions of…

## One Citation

Monotone methods in counterparty risk models with nonlinear Black–Scholes-type equations

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