Fair valuation of mortgage insurance under stochastic default and interest rates

Unlike most studies in the literature, in this study, we incorporate three main factors into the pricing method of mortgage insurance: interest rate, housing price, and hazard rate (default risks). The empirical analysis highlighted that the interest rate and housing price are positively correlated during July 2004 to November 2016 because of the monetary policy over this period. Subsequently, in the risk-neutral pricing framework, mortgage insurance of the fixed-rate mortgage is priced using a Monte Carlo simulation approach. The sensitivity analysis indicated that interest rate, housing price, and default rate are important factors for mortgage insurance. Moreover, because our model can measure the risks of the interest rate and hazard rate, insurance companies can use this model to price mortgage insurance to avoid a condition in which the insurance company does not have sufficient reserves to support compensation.