An approximate closed formula for European Mortgage Options

TL;DR

This paper develops a close-form approximation for pricing European mortgage options using lognormal distribution matching, enabling efficient computation with high accuracy validated against Monte Carlo simulations.

Contribution

It introduces a novel approximation method for mortgage option pricing based on moment matching and lognormal distributions, simplifying calculations.

Findings

Close-form approximation closely matches Monte Carlo results.

Method works well under various market conditions.

Provides a computationally efficient alternative to simulation.

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.