Solving Semi-Linear Risky-Closeout PDE by Discount Boundary Optimization

23 Pages Posted: 14 Feb 2015 Last revised: 23 Feb 2015

Date Written: February 23, 2015

Abstract

We consider a non-linear PDE that appears in a number of contexts including a one-way CSA, CVA with risky closeout, option pricing with differential borrowing and lending rates, accounting-consistent valuation, and constrained cash supply. We show that its solution is given as the minimum of solutions of certain related linear PDEs. An efficient numerical method in any number of dimensions that is based on our representation is presented.

Keywords: semi-linear PDE, non-linear PDE, one-way CSA, CVA with risky closeout, option pricing with differential rates, accounting-consistent valuation, FVA, CVA, XVA, DVA, obstacle problem

Suggested Citation

Piterbarg, Vladimir, Solving Semi-Linear Risky-Closeout PDE by Discount Boundary Optimization (February 23, 2015). Available at SSRN: https://ssrn.com/abstract=2564152 or http://dx.doi.org/10.2139/ssrn.2564152

Vladimir Piterbarg (Contact Author)

NatWest Markets ( email )

250 Bishopsgate
London, EC2M 4AA
United Kingdom

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