Housing Debt, Employment Risk and Consumption

We consider the interaction between the risk of unemployment, random house prices, consumption and savings. A critical decision is that of refinancing house purchase, up to 100% mortgages are possible. There is also a fixed transaction cost of refinancing. In a CARA framework we derive the value function for a finite horizon, the policy of refinance and the consumption function. Either there is a maximum mortgage or a zero mortgage depending on interest rates, house prices and the transaction cost. The consumption function is linear in wealth and in the uncertainty caused by employment status and house prices of the future. Since there is either 100% or 0% equity withdrawal, consumption jumps when there is refinancing.