  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.

Computational Finance