A real option approach to the valuation of the default risk of residential mortgages

A significant share of many commercial banks' portfolios consists of residential mortgage loans provided to individuals and families. This paper examines the default and rational prepayment risk of single-borrower (residential) mortgage loans based on an option pricing model that captures the skewness and kurtosis of the house prices returns' distribution via the shifted lognormal distribution. Equilibrium option-adjusted credit spreads are obtained from the implementation of the model under plausible values of the relevant parameters. The methodology involves numerical experiments, using a shifted binomial tree model by Haathela and Camara and Chung, to evaluate the effects of the loan-to-value (LTV) ratio, asset volatility, interest rates, and recovery costs on mortgage valuation. Findings indicate prepayment risk significantly influences loan value, as it limits upside potential, while LTV and volatility directly impact default risk. The shifting parameter (θ) in the asset distribution proves essential for accurate risk assessment. Conclusions emphasize the need for mortgage underwriting to consider specific asset characteristics, optimal loan structures, and prevailing risk-free rates to avoid underestimating risk. This model can aid in the more robust pricing and management of mortgage portfolios, especially relevant in regions with substantial mortgage-backed exposure, such as the European banking system.