Research On The Pricing Model And Numerical Implementation Of Credit Derivatives

Derivatives growth in the latter part of the 1990s continues along at least three dimensions. Firstly, new products are emerging as the traditional building blocks forwards and options-have spawned second and third generation derivatives that span complex hybrid, contigent, and path-dependent risks. Secondly, new applications are expanding derivatives use beyond the specific management of price and event risk to the strategic management of portfolio risk, balance sheet growth, shareholder value, and overall business performance. Finally, derivatives are being extended beyond mainstream interest rate, currency, commodity, and equity markets to new underlying risks including catastrophe, pollution, electricity, inflation, and credit. Credit derivatives fit nearly into this three-dimensional sheme. It is more complex class of path dependence provides a tailor-made credit risk mangement tools.Credit derivatives pricing and their risk management is a hotspot of current's financial engineering. Because of heterogeneous characteristics of the underlying asset, the analytic solutions of credit derivatives price problems can only be got under some very simple assumptions. Often the analytical solutions contain high-dimensional convolutions and high-dimensional integrations, which need intensive computing resources to be calculated. It limits the pricing and risk management activities of multiply underlings credit derivatives.This paper uses Monte Carlo simulation, importance sampling algorithm, principal component analysis method and the differential evolution algorithm to broaden the numerical researches for credit derivatives pricing and risk management.For the multiply underlying credit derivatives, we propose an iterative algorithm which can use small samples to estimate the default correlations of the underlying pool; then, we summarize the methods which can be used to estimate the underlying assets' default intensity functions and algorithms can be used to simulate the correlated default times of the underlying assets. We discuss the importance sampling algorithm in the Monte Carlo simulation for the credit derivatives pricing problem deeply. We propose a multi-component variable variance importance sampling algorithms to fix the deficiency of the one component constant variance importance sampling algorithm, and then verify the consistency of the algorithm from theoretical and numerical perspectives. Using the multi-component variable variance importance sampling algorithm and differential evolution algorithm, we propose a new objective functions which can be used to duplicate the implied default correlation curves of credit derivatives. And it also can be used to manage the risk of credit derivatives. We propose a complete algorithm which can be used to solve the duplication problem of implied default correlation curve, and we give an empirical study which using simulating data.The research shows that using multi-component variable variance importance sampling algorithm and differential evolution algorithm to study the credit derivative pricing and risk management problems have a certain degree of accuracy, efficiency and stability advantages. The multi-component variable variance importance sampling algorithm can be used in more extreme circumstances, and it can estimate the default probability more reasonable and give a more accurate spread of credit derivatives. The iterative algorithm which used to estimate the default correlation matrix considers the effects of the two underlying changing correlations and other underlying assets'changing correlations more comprehensively. When we facing the credit derivative risk management problems, we can balance the two effects more suitable. When using the differential evolution algorithm to duplicate the implied correlation curves, we should use the weighted objective function and elite evolution strategy. These conclusions have some useful effects for the pricing of complex credit derivatives and risk management of credit derivatives.