MVA: Initial Margin Valuation Adjustment by Replication and Regression

TL;DR

This paper introduces a new valuation adjustment called MVA for initial margin costs in derivatives, extending existing frameworks, and proposes a regression-based method for efficient computation.

Contribution

It extends the semi-replication framework to include initial margin costs and develops a regression technique for fast MVA calculation.

Findings

MVA can be integrated into derivative valuation models.

Regression methods significantly reduce computational costs.

The approach is practical for real-world risk management.

Abstract

Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010, Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of regulatory capital (KVA) (Green2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of (Burgard2013a), itself later extended by (Green2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose a computationally efficient approach to the calculation of MVA through the use of regression techniques, Longstaff-Schwartz Augmented Compression (LSAC).