Stochastic Evolution Equations in Portfolio Credit Modelling

Nick Bush · Ben M. Hambly · Helen Haworth · Lei Jin · Christoph Reisinger

59 citations0/0 files storedSIAM Journal on Financial Mathematics

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Stochastic processes and financial applications Credit Risk and Financial Regulations Risk and Portfolio Optimization

Abstract

We consider a structural credit model for a large portfolio of credit risky assets where the correlation is due to a market factor. By considering the large portfolio limit of this system we show the existence of a density process for the asset values. This density evolves according to a stochastic partial differential equation, and we establish existence and uniqueness for the solution taking values in a suitable function space. The loss function of the portfolio is then a function of the evolution of this density at the default boundary. We develop numerical methods for pricing and calibration of the model to credit indices and consider its performance before and after the credit crunch.

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References

1974ON THE PRICING OF CORPORATE DEBT: THE RISK STRUCTURE OF INTEREST RATES*2007Brownian Motion and Stochastic Calculus 1999Continuous Martingales and Brownian Motion 1976VALUING CORPORATE SECURITIES: SOME EFFECTS OF BOND INDENTURE PROVISIONS 2001Term Structures of Credit Spreads with Incomplete Accounting Information 2001The term structure of credit spreads with jump risk 2000Pricing Financial Instruments: The Finite Difference Method 2001Solution of stochastic partial differential equations using Galerkin finite element techniques

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