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

This estimate projected in 2030 is based on the following conservative assumptions: the elderly population in Europe is 124 million; the overall home ownership in the population is 71%; average house price is €210,000; a 22% loan-to value and annual sales of 1/2%; no inflation.

See, for example, Szymanoski (1994) and Wang et al. (2007).

Examples include Ambrose and Buttimer (2000), Bardhan et al. (2006) and Liao et al. (2008).

There are localized effects in different cities and regions and HPI do not capture all of the semi-idiosyncratic risk that appears in housing. To consider basis risk, we also analyze some city/region indices in this study.

Examples include Kau and Keenan (1996), Chen et al. (2010) and Chang et al. (2011).

Chan and Maheu (2002), Eraker (2004), Maheu and McMcurdy (2004), Duan et al. (2006, 2007) and Daal et al. (2007) all consider the GARCH jump model for dealing with equity returns and find that accommodating for jumps effect in the log return and volatility considerably improves the model’s fit for the return data of equity markets. Among them, Eraker (2004) and Duan et al. (2006, 2007), Chan and Maheu (2002), Maheu and McMcurdy (2004) and Daal et al. (2007) consider a dynamic jump setting. Duan et al. (2006) extended theory developed by Nelson (1990) and Duan (1997) by considering limiting models for the GARCH-jump process. In additional, Duan et al. (2007) provide empirical test of GARCH-jump model to price options, using data on S&P 500 index and the set of European options written on S&P 500 index. Further, Daal et al. (2007) proposed asymmetric GARCH-jump models that synthesize autoregressive jump intensities and volatility feedback in the jump component to fit for the dynamics of the equity returns in the US and emerging Asian stock markets. However, different to these literatures, we deal with house price return dynamics instead of equity returns. Thus, we further consider the ARMA-GARCH jump framework.

The discrepancy between the returns on the mortgaged property.

The Federal Home Loan Bank Board approved ERMs in 1979.

The most common types of payment options for equity-release products are lump sum (roll-up), terms, lines of credit, modified terms (combining lines of credit and term payments), tenure and modified tenure (combining lines of credit and tenure). Given that the roll-up mortgage has become the most popular payment option, our ongoing analysis focuses on this type of mortgage.

Maheu and McCurdy (2004) consider the jump setting under a constant conditional mean of GARCH model. We deal with a jump ARMA-GARCH model and the likelihood function for parameter estimation is reconstructed.

Equation (18), (19) and (20) involve an infinite sum over the possible number of jumps, N_t. In practice, for our model estimated we found that the conditional Poisson distribution had zero probability in the tail for values of N_t ≥ 10 and the likelihood and the parameter estimates converge.

Although not reported here, the parameter estimates of the models are available upon request.

AIC = −2/obs. ln(likelihood) + 2/ obs. × (No. of parameters) (Akaike 1973); BIC = −2/ obs. ln(likelihood) + ([No. of parameters] × ln[obs.]) / obs.; obs. is the sample size.

The stochastic processes of these models are available upon request.

See, for example, Gerber and Shiu (1994), Bühlmann et al. (1996), Siu et al. (2004), Li et al. (2010) and Chen et al. (2010).

We use the UK mortality data from 1950 to 2006 according to the human morality database (HMD) and the data ages cover from age 60 to 100. Therefore, the mean age is 80 in our model calibration.

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Examples include Merton (1973), Rabinovitch (1989), Turnbull and Milne (1991) and Amin and Jarrow (1992).