Enhanced Modelling of Valuation Adjustments for Comprehensive Financial Risk Management

Abstract

The 2007-2008 global financial crisis provided a wake-up call for the financial industry that some assumptions underlying the classical risk-neutral valuation framework for financial derivatives are violated. Especially the assumption related to the absence of Counterparty Credit Risk, i.e., the risk that a counterparty goes in default. This gave rise to various Valuation Adjustments (xVAs) to account for aspects of trading financial derivatives which are not part of the risk-neutral framework. Appropriate assumptions and modelling choices must be made when developing an xVA model, such that the computed values are fit for purpose while keeping the computations practically feasible.

This thesis proposes refined xVA modelling techniques that enhance risk prediction accuracy for financial derivatives, addressing gaps in traditional Valuation Adjustment methodologies. We challenge assumptions related to Wrong-Way Risk (WWR) and the volatility smile, while guaranteeing the efficient computation of exposures, metrics and associated risks.

Chapter 2 explores dynamic Credit Valuation Adjustment (CVA) hedging, starting in a Black-Scholes setting, followed by a Merton jump-diffusion model to incorporate volatility smile. Chapters 3 and 4 focus on the relevance and efficient computation of WWR in Funding Valuation Adjustment (FVA) on linear interest rate and foreign exchange derivatives. We propose a method to split exposures into independent and WWR components and approximate the latter. Chapter 5 introduces a novel model for smile-aware xVA for linear and early-exercise IR derivatives.

These enhancements of the xVA modelling landscape give rise to interesting mathematical research at the cross-section of practically motivated work and academically relevant research.