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

Ferhana Ahmad; Ben M Hambly; Sean R Ledger

doi:10.1016/j.spa.2017.12.002

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

Ferhana Ahmad, Ben M Hambly, Sean R Ledger^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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
Number of pages	29
Journal	Stochastic Processes and their Applications
Early online date	9 Jan 2018
DOIs	https://doi.org/10.1016/j.spa.2017.12.002
Publication status	E-pub ahead of print - 9 Jan 2018

Keywords

Measure-valued process
Mortgage-backed securities
Particle system
Stochastic PDE

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10.1016/j.spa.2017.12.002

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AB - 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

KW - Measure-valued process

KW - Mortgage-backed securities

KW - Particle system

KW - Stochastic PDE

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