Derivatives pricing with xVAs

Abstract

Derivatives pricing changed drastically in 2007-2008, following the financial crisis. The failure of the Lehman Brothers refuted the myth that ”AAA” rated financial institutions cannot default. Basel III was introduced and implemented to reinforce existing financial market regulations and counterparty credit risk became the primary subject of debate in financial markets’ regulations. Prior to the financial crisis, derivatives pricing had its assumptions aligning to those from the Black-Scholes-Merton model. This model assumes that default risk is absent, but this financial crisis highlighted that in reality, this is not true. In this dissertation,we research and offer an analysis of derivatives pricing following the financial crisis wherebywe extend the Black-Scholes-Merton model to incorporate default risk, collateral, funding costs, regulatory capital, and initial margin through the implementation of the model of Burgard and Kjaer called the semi-replication strategy. The primary emphasis would therefore be on the derivation of xVAs. We also evaluate regulatory capital and initial margin methodologies which are used to compute KVA and MVA, respectively.