A stochastic partial differential equation model for the pricing of mortgage-backed securities |
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| Authors: | F Ahmad BM Hambly S Ledger |
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| Institution: | 1. Suleman Dawood School of Business, Lahore University of Management Sciences, Lahore, Pakistan;2. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Oxford OX2 6GG, UK;3. Heilbronn Institute, University of Bristol, Howard House, Bristol BS8 1SN, UK |
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| 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. |
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| Keywords: | Stochastic PDE Particle system Measure-valued process Mortgage-backed securities |
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