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 journalArticle (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 languageEnglish
Number of pages29
JournalStochastic Processes and their Applications
Early online date9 Jan 2018
DOIs
Publication statusE-pub ahead of print - 9 Jan 2018

Keywords

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

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