MODELLING MORTGAGE INSURANCE: AN OPTION PRICING APPROACH

Abstract

Mortgage Insurance, being a new concept in Singapore, requires the resolution of pricing issues before it can be implemented. This study posits a scientific methodology backed by the well-known Black Scholes Option Pricing Theory to provide a pricing mechanism for mortgage insurance. The posited framework not only employed the versatile explicit finite difference scheme but also a mixed backward and forward pricing methodology involving the Monte Carlo Simulation method to circumvent the general path dependency problem present in most ARM. More interestingly is that the framework prices a default, a prepayment and an insurance option simultaneously by a system of partial differential equations to show the interacting effects of the three options embedded in a preferential rate mortgage. Results show that the interacting effects do have significant implications on the overpricing of embedded options. In the interests of realism, suboptimal termination and foreclosure discounts are included in the model. Results from analysis of foreclosure discounts have showed that insurers should only be concerned with the foreclosure process when there are substantial increases in foreclosure discounts over 15%. Analyses of the various economic parameters in the model also show that insurance prices are most sensitive to dynamic changes in housing market.