Corrected XVA Modelling Framework and Formulae for KVA and MVA

TL;DR

This paper refines the XVA modeling framework by correcting key errors in the valuation adjustments for KVA and MVA, incorporating bilateral credit risk and funding costs for more accurate derivative pricing.

Contribution

It provides corrected formulae for KVA and MVA, enhancing the accuracy of XVA models by addressing previous errors and clarifying the framework.

Findings

Corrected the formulas for KVA and MVA.

Clarified the inclusion of bilateral credit risk and funding costs.

Improved the accuracy of derivative valuation adjustments.

Abstract

We discuss and clarify the XVA modelling framework specified in the paper "MVA by replication and regression" (Risk Magazine, May 2015) for including bilateral credit risk and funding costs in derivative pricing, and in doing so we rectify two key errors in the valuation adjustments accounting for costs of capital and initial margin, and present corrected formulae for KVA and MVA.