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A stochastic partial differential equation model for the pricing of mortgage-backed securities. (English) Zbl 1416.91364

Summary: We develop a dynamic structural model for the wealth of individual mortgagors in a mortgage pool. We model the process of default and prepayment and, by taking a limit as the pool size goes to infinity, derive a stochastic partial differential equation (SPDE) which can be used to describe the evolution of the loss process from the pool. We prove existence and uniqueness of solutions to this SPDE and show how our model is able to capture, in a flexible way, the prices of credit risky tranches of mortgage-backed securities under different market conditions.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
91G40 Credit risk
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