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Mortgage Backed Securities (MBS) are a type of security backed by mortgages as the underlying asset. This is achieved through a process called securitization, where specific mortgages are grouped together and separated from the bank’s other assets, and then sold to investors.

One of the risks for investors in MBS is mortgage prepayments made by the borrowers of the underlying mortgages. This risk arises due to the uncertainty of the expected cash flows to be distributed among the investors. There is a correlation between falling market interest rates and an increase in prepayments. When market interest rates fall, borrowers have an incentive to refinance their mortgages at lower interest rates, leading to higher prepayment rates.

The Public Securities Association (PSA) model is recognized as a standard benchmark for estimating prepayment rates in MBS. In this paper, we have introduced models to generate time points for prepayments and compare how well these models match with the PSA model. Some of these models determine the timing of each prepayment event using an exponentially distributed Poisson process, while one model employs the Gamma distribution. Additionally, we introduce a strategy where prepayment is strategically triggered by whether the market rate falls below the contract rate. In that strategy, we investigate when it is most beneficial to make a prepayment.

The results show that among the models employing random generation of prepayment events, the Gamma distribution best aligns with the PSA rule. Regarding the strategic prepayment strategy, our findings suggest that it is most advantageous to make prepayments early in the mortgage term, aligning with the most rational behavior as well.