Modeling Housing Price Dynamics and their Impact on the Cost of no-Negative-Equity-Guarantees for Equity Releasing Products

We investigate model risk in pricing no-negative-equity guarantees (NNEGs) with the aim of identifying the housing risks involved in equity-release products. To analyze the regional and local effect in the house price modeling, we evaluate different models using the house price index (HPI) based on the cities of London, Manchester and Coventry and the UK nationwide HPI respectively. The ARMA-GARCH jump model that can capture the characteristics of jump persistence, autocorrelation and volatility clustering are proposed according to the model fittings. To investigate the model risk on the cost of NNEGs, we then derive the risk-neutral valuation framework using the conditional Esscher transform technique (Bühlmann et al. 1996). Our numerical analyses reveal that the housing model risk affects the costs of NNEGs significantly. In addition, the cost of NNEGs is significantly different for different cities due to localized effect. Therefore, the basis risk is large enough to matter when pricing NNEGs.