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
Original language | English |
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Number of pages | 29 |
Journal | Stochastic Processes and their Applications |
Early online date | 9 Jan 2018 |
DOIs | |
Publication status | E-pub ahead of print - 9 Jan 2018 |
Keywords
- Measure-valued process
- Mortgage-backed securities
- Particle system
- Stochastic PDE