A stochastic partial differential equation model for the pricing of mortgage-backed securities

F. Ahmad, B.M. Hambly and S. Ledger

Stochastic Processes and their Applications, 2018, vol. 128, issue 11, 3778-3806

Abstract: 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.

Keywords: Stochastic PDE; Particle system; Measure-valued process; Mortgage-backed securities (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2017.12.002

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