Funding, repo and credit inclusive valuation as modified option pricing

TL;DR

This paper develops a comprehensive valuation framework for OTC claims that integrates credit, funding, and liquidity risks using advanced nonlinear PDEs and FBSDEs, providing analytical solutions for certain cases.

Contribution

It introduces a holistic valuation approach that combines multiple risk factors into a unified model, with analytical solutions for benchmark claims.

Findings

Analytical solution for a benchmark vulnerable claim using Black-Scholes formula.

Enables detailed valuation, stress testing, and sensitivity analysis.

Integrates credit, funding, and liquidity risks into a unified nonlinear model.

Abstract

We take the holistic approach of computing an OTC claim value that incorporates credit and funding liquidity risks and their interplays, instead of forcing individual price adjustments: CVA, DVA, FVA, KVA. The resulting nonlinear mathematical problem features semilinear PDEs and FBSDEs. We show that for the benchmark vulnerable claim there is an analytical solution, and we express it in terms of the Black-Scholes formula with dividends. This allows for a detailed valuation analysis, stress testing and risk analysis via sensitivities.