A Computational Approach to Hedging Credit Valuation Adjustment in a Jump-Diffusion Setting

TL;DR

This paper explores dynamic hedging of Credit Valuation Adjustment (CVA) in jump-diffusion models using Monte Carlo simulations, providing insights into risk management and the importance of proper hedging strategies.

Contribution

It introduces a framework for hedging CVA in jump-diffusion settings and compares strategies in Black-Scholes and Merton models, including analytical insights.

Findings

Hedging CVA is essential to avoid expected losses.

In Black-Scholes, stock-based hedging suffices.

In jump-diffusion, additional options are needed for proper hedge.

Abstract

This study contributes to understanding Valuation Adjustments (xVA) by focussing on the dynamic hedging of Credit Valuation Adjustment (CVA), corresponding Profit & Loss (P&L) and the P&L explain. This is done in a Monte Carlo simulation setting, based on a theoretical hedging framework discussed in existing literature. We look at hedging CVA market risk for a portfolio with European options on a stock, first in a Black-Scholes setting, then in a Merton jump-diffusion setting. Furthermore, we analyze the trading business at a bank after including xVAs in pricing. We provide insights into the hedging of derivatives and their xVAs by analyzing and visualizing the cash-flows of a portfolio from a desk structure perspective. The case study shows that not charging CVA at trade inception results in an expected loss. Furthermore, hedging CVA market risk is crucial to end up with a stable trading strategy. In the Black-Scholes setting this can be done using the underlying stock, whereas in the Merton jump-diffusion setting we need to add extra options to the hedge portfolio to properly hedge the jump risk. In addition to the simulation, we derive analytical results that explain our observations from the numerical experiments. Understanding the hedging of CVA helps to deal with xVAs in a practical setting.