Reviewing a framework to price a credit risky derivative post the credit crisis
The period between 2008 and 2009 was an interesting and dramatic time for financial markets. This period marked the beginning of the financial tsunami that would plague global markets for many years to come. This economic meltdown had massive effects on many everyday issues such as house prices, interest rates and inflation. Investment banks were also affected with numerous investment banks either defaulting or being taken over by the U.S. Federal Reserve to avoid default. This group of investment banks include names such as Lehman Brothers, Bear Sterns, Fannie Mae, Freddy Mac and many more. The myth of “too big to fail” was tested and failed because of the number of banks that were allowed to default during the crisis. Many things have changed because of the crisis. One area in finance that has changed is the pricing of financial derivatives. The realisation that huge investment banks can default has dried up the liquidity in capital markets. Therefore banks cannot borrow a shortfall of cash at a risk-free rate anymore but rather at a significant spread over the risk-free rate. The risk-free rate is a core concept of derivative pricing. If investment banks cannot borrow and lend at the risk-free rate then the Black-Sholes-Merton theory laid down in the 1970’s may not be applicable post the credit crisis. The aim of this dissertation is to review the framework of Piterbarg, Burgard and Kjaer to price a general derivative post the credit crisis. This review includes a variety of numerical methods to implement the framework.
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 2014.