An Approximate Closed Formula for European Mortgage Options

Authors

  • A. M. Lopez Galvan

DOI:

https://doi.org/10.5540/tcam.2023.024.03.00395

Keywords:

Mortgages option, mortgages rates, moment matching

Abstract

The aim of this paper is to investigate the use of close formula approximation for pricing European mortgage options. Under the assumption of logistic duration and normal mortgage rates the underlying price at the option expiry is approximated by shifted lognormal or regular lognormal distribution by matching moments. Once the price function is approximated by lognormal distributions, the option price can be computed directly as an integration of the distribution function over the payoff at the option expiry by using Black-Scholes-Merton close formula. We will see that lower curvature levels correspond to positively skewness price distributions and in this case lognormal approximation leads to close parametric formula representation in terms of all model parameters. The proposed methodologies are tested against
Monte Carlo approach under different market and contract parameters and the tests confirmed that the close form approximation have a very good accuracy.

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Published

2023-07-20

How to Cite

Lopez Galvan, A. M. (2023). An Approximate Closed Formula for European Mortgage Options. Trends in Computational and Applied Mathematics, 24(3), 395–410. https://doi.org/10.5540/tcam.2023.024.03.00395

Issue

Vol. 24 No. 3 (2023)

Section

Original Article

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