MVA Transfer Pricing

TL;DR

This paper develops a comprehensive framework for pricing OTC derivatives with initial margin considerations, integrating MVA into fair value calculations and exploring transfer mechanisms to clients, supported by numerical examples.

Contribution

It introduces an extended PDE approach for all-in fair value including MVA and links it to external IM models like ISDA SIMM, advancing derivative pricing theory.

Findings

MVA can be transferred to clients via liability-side pricing.

The PDE captures IM components, including vega and curvature.

Numerical examples illustrate MVA's impact on swap and equity portfolio pricing.

Abstract

This article prices OTC derivatives with either an exogenously determined initial margin profile or endogenously approximated initial margin. In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential equation is derived and solved for an all-in fair value, decomposable into coherent CVA, FVA and MVA. For uncollateralized customer trades, MVA can be transferred to the customer via an extension of the liability-side pricing theory. For BCBS-IOSCO covered OTC derivatives, a market maker has to charge financial counterparties a bid-ask spread to transfer its funding cost. An IM multiplier is applied to calibrate to external IM models to allow portfolio incremental pricing. In particular, a link to ISDA SIMM for equity, commodity and fx risks is established through the PDE with its vega and curvature IM components captured fully. Numerical examples are given for swaps and equity portfolios and offer a plausible attribution of recent CME-LCH basis spread widening to elevated MVA accompanying dealers' hedging of customer flows.