基于提前支付强度过程的抵押贷款定价与均衡

Valuation and Equilibrium of Mortgage:An Intensity-based Approach

基于提前支付强度过程考察了固定利率抵押贷款合同的定价和市场均衡问题。将均衡问题描述成代表性抵押人与市场之间的博弈。均衡由市场决定的内生抵押贷款利率和抵押人的最优再融资策略描述。在时齐Markov链利率及正线性比例再融资成本假设下,抵押人的规划问题可以简化成一个仅包含三个离散状态变量的Markov决策链,且一定存在唯一解。从而,均衡可由一个抵押利率决定函数和抵押人的最优再融资策略组成。一个简单的数值例子说明了计算均衡的迭代算法。结果表明,抵押人选择再融资往往是不明智的短视行为。

Based on prepayment intensity process, the valuation of fixed-rate mortgage contracts is studied and an equilibrium model is built with the specification of a game between the representative mortgagor and the market whose optimal strategy are about the endogenous mortgage rates and whether to refinance a new contract or continue with the current one, respectively, Under the assumption of the rate process of time-homogeneous Markov chain and positive linear refinancing cost, the dynamic programming problem of the mortgagor is simplified to a Markov decision chain with only three discrete state variables which is proved, by standard dynamic programming theory, to have a unique solution. Thus, the equilibrium can be given by a pair of the endogenous rate and the optimal refinancing strategy of the mortgagor. A simple numerical example with an iteration algorithm is finally provided to show how to compute the equilibrium. The results show that the mortgagor is usually too hasty to refinance, thus refinancing is typically a myopic behavior.