Pricing models for credit derivatives

Abstract

Abstract The project is an empirical research on the implementation of various credit risk models developed over the past several years. The pricing methodologies covered are 1. Reduced Form Modelling using Hull White Model for Credit Default Swaps 2. Structural Models 3.Compound Option Methodology. These three methods cover the broad spectrum of the methods used to price credit. The parameters of credit were found out using these methodologies and various tests were carried out to explain the extremely interesting patterns found. The main input data used were 1. Real Credit Default Swap market prices 2.The stock prices and 3.The prices on the option on the equities, of five European and US companies which form a wide band of credit ratings and for which CDS and option markets have enough liquidity to ensure that the results are accurate. Thus this research looks at the data available in the bond market, the equity market and the derivatives market to find out the credit properties of the companies in the sample. The methodology used was the empirical analysis of the values predicted by the models and checking their consistency with each other. The data from the three markets was sourced from several data service providers and from several government and company websites. For the implementation of the Hull-White model, numerical integration was employed and a solution was arrived at by numerical solving using Visual Basic and Excel. The term structure of the distance to default was found out for each company for a period of 180 days for 5 different maturities. For the implementation of the Structural model, several assumptions were made because of the severe constraints on data and the simplistic way in which the model defines the data. The implementation was based on the standard option pricing methodology for pricing credit as given by Merton. The equity data was used as a base to find out the Asset volatility, the Value of the assets of the company and the probability of default. For the pricing of credit using compound option methodology as outlined in the latest Hull White (2004) paper on volatility skews. This involved modelling the option on the equity as a compound option on the assets of the company and hence using the standard formula given by Geske to price the compound option. As the pricing equation for a single option gives an equation connecting the variables Debt ratio and the asset volatility, the pricing equation should be applied on two different stock options to generate two equations in two variables solving which would give us the values of the debt ration and the asset volatility. Excel add-ons in VB were used to find the values of the Bi-variate distributions required for these pricing equations. Excel was used to solve the equations but it could not find a single solution. We were able to find very significant results from the implementation of the Hull White model which was able to predict the credit properties of the Reference entities quite well. The Merton Model implementation gave positive results in terms of trends but absolute values of the Default probabilities and the spreads were under estimated. Numerical solution of the Compound option Equation did not give results which were consistent with the actual market values although the real issue might have been the consistency of the data used as inputs. The conclusion is that most models of credit are highly theoretical in nature and give consistent results only when applied in a highly constrained manner. Applying the models on actual market data might give us an idea about the trends but in terms of absolute numbers, the models are not very consistent with the actual results. Two of the models employed were based on papers published in the last 2-3 years and hence implementation of these models has not been attempted outside the research desks of investment banks. Hence, the practical assumptions and surrogates which could be used to simplify the formulation of the models have not received much attention and, hence, are not found in literature. This has severely impaired the smooth progress of the research and this scenario will certainly change in the next few years when these models become more popular. Hence the scope for studying credit characteristics based on these models will become wider as and when the implementation of the concepts are more crystallized in practice.