Derivatives pricing with xVAs
Date
2021
Authors
Tshehla, Godfrey
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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.
Description
A dissertation submitted to the School of Computer Science and Applied Mathematics, University of the Witwatersrand, in fulfilment of the requirements for the degree of MSc in Computational and Applied Mathematics, 2021