Default and prepayment behaviour as competing risks

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It has been increasingly recognised that default and prepayment behaviour are best viewed as competing risks, where exercising one option precludes the exercise of the other (Deng et al. 1996; Pavlov 2001, Deng et al. 2000; Clapp et al. 2001; Ambrose & LaCour Little 2001; Colhoun & Deng 2002). This work has been based on either the competing risk proportional hazard models, or the multinomial logit model. The research generally finds that the option theoretic approach is important and can explain household behaviour, but that trigger events and personal circumstances also have explanatory value, and that there is a significant measure of unexplained heterogeneity. Speculations on the nature of the unobservable factors have ranged from different attitudes to risk to variations in financial competence/sophistication (Deng et al. 2000). However, the use of a competing risk methodology has also resulted in a number of important improvements to estimation and new economic insights.

The use of a competing risk methodology has made significant improvements in the ability to predict mortgage terminations (Deng et al. 2000; Clapp et al. 2001). The approach also removes various biases in estimation and makes for more efficient and consistent parameter estimates (Pavlov 2001). Modelling unobserved heterogeneity has had a particularly important impact, and has actually enhanced the explanatory power of the variables reflecting the embedded call and put options in mortgage debt (Deng et al. 2000); though not all studies have corrected for this. New results have emerged from correctly identifying the competing risks. In particular, recognising household mobility and adjustments in housing demand, as a competing risk has led to different estimates of the influence of key variables on mortgage termination (Pavlov 2001; Ambrose & Buttimer 2000).

Household mobility is something that might be better explained by borrower characteristics and changes in economic circumstances than changes in the value of the mortgage. Generally, this is what the research finds. Pavlov (2001) notes that the value of the mortgage has no significant effect on the mobility decision, though the estimated model contains no borrower characteristics. Clapp et al. (2001) notes the smaller effect of income on prepayment if mobility induced refinancing is not separately identified. Clapp et al. find that financial factors are important for prepayment, but not for the moving or the default decision. Other socioeconomic factors such as rates of divorce or unemployment have been found to be significant 'trigger events' and indicate the importance of liquidity constraints on both prepayment and default (Deng et al. 1996, 2000).14

Some research has indicated that it is useful to stratify the sample under study, for example by wealth or income. Deng et al. (1996) found that in terms of their propensity to default low income households were more sensitive to falling equity values, The 'ruthless' default model appeared most applicable to the very wealthiest households. Deng et al. (2000) note two clusters (high risk and low risk) of unobserved heterogeneity. This might represent the division between sophisticated and unsophisticated borrowers, though again the absence of several key variables (e.g. credit history) must leave the interpretation of this finding open to debate. A further interesting basis for segmentation is households who default for a second time. This group have had their mortgages re-instated only to possibly default again. Ambrose & Buttimer (2000) find that the economic factors that predict first defaults do not have the same influence on second defaults, for example interest rates had opposite effects.

Given the above, a key question is how far the competing risk approach confirms the option theoretic view of prepayment and default decisions? All of the competing risk studies reinforce the importance of the option theoretic perspective. Deng et al. (2000) find that controlling for unobserved heterogeneity actually improves the explanatory power of financial variables representing the call and put options. Competing risk studies highlight the differential influence of financial factors upon the prepayment, default and the moving decision. Some studies find that financial factors influence prepayment but have little effect on default (Clapp et al. 2001; Ambrose & Buttimer 2001). Deng et al. note that unobserved heterogeneity is more important for prepayment than default. There is a general view in the literature that there are aspects of termination behaviour that still require explanation.

Discussion in previous chapters has focused upon signalling and screening in the mortgage market, for example the role of points in screening for more mobile borrowers more likely to prepay. Interestingly, a number of studies have included mortgage points as an explanatory variable. Empirical tests confirm the expected relationship between points and mobility and prepayment, that is lower points correspond with a higher probability of prepayment (Pavlov 2001; Clapp et al. 2001). Mortgage term might also act as a signalling device with longer terms being favoured by less mobile borrowers (Clapp et al. 2001). The loan-to-value ratio at origination is a variable that can also reflect upon information asymmetry. Deng et al.

(2000) noted that if borrowers know more about the price characteristics of their property (e.g. volatility) then the mortgage may represent an under-priced option to be exploited by higher gearing.

The competing risk studies have adopted a variety of econometric techniques. The most sophisticated is perhaps the modelling which involves the simultaneous determination of default and prepayment probabilities while controlling for unobserved heterogeneity, that is the so called HHSM model applied by Deng et al. (2000) and Ambrose & LaCour Little

(2001). Clapp et al. (2001) apply a multinomial logit model but find little difference in the estimates compared to a standard Cox Proportional Hazards model. The importance of unobserved heterogeneity has been quite clearly demonstrated by these studies. However, there is a need to use richer databases that would allow for otherwise omitted variables (e.g. credit histories), incorporate post-origination data on incomes and housing equity and cover periods when defaults are more significant. There is much further research to be done in this important area of mortgage market economics.

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