Research On Refinancing,prepayment And Default Risks Of Residential Mortgage Loan

Nowadays,residential mortgage loan has been one of the most important credit assets of financial institutions,and buying houses through the mortgage has also become the main way of buying houses for the buyer group.However,affected by macroeconomic environment,mortgage rate,the size of the population and housing prices,the mortgage market is also facing some credit risk problems in the process of booming development,such as refinancing,prepayment and default.Accurately characterizing and measuring these credit risks is a concern of borrowers,lenders and investors in the mortgage market.This paper considers the influence of macroeconomic factors on borrowers’ behaviors and uses credit risk models with regime switching to depict borrowers’ refinancing,prepayment and default behaviors.In theory,the results of the paper enrich the existing asset valuation model,and further expand the risk measurement methods.In application,the model and conclusion can help borrowers make reasonable decisions of repayment,and enable lenders and investors to optimize asset allocation and make better investment choices.The specific results are as follows:First,we investigate an optimal refinancing problem for an interest-only mortgage,where market mortgage rate is defined as the geometric Brownian motion with regime switching.We obtain the optimal refinancing strategy and verify that this strategy only depends on the quotient between the market mortgage rate and the borrowing rate.We show that the optimal refinancing strategy is of threshold type.By reducing the two-dimensional optimal refinancing problem to a one-dimensional problem,we obtain the system of equations that the value function satisfies.The explicit expression of the value function and the system of equations satisfied by the threshold values are obtained when the Markov process describing macroeconomic environment has one or two states.We present some numerical results to illustrate the influence of the model parameters on the optimal refinancing strategy.Second,we develop a valuation model for mortgage pass-through securities with partial prepayment risk using the reduced form approach.For each mortgage in the pool,the occurrence time of prepayments is modeled by the jump times of a Cox process.When partial prepayment occurs,the ratio of partial prepayment amount to outstanding principal is described by a stochastic process.Under these conditions,we obtain valuation formulas of mortgage pass-through securities without and with regime switching,respectively.Based on these results,we also obtain the expected present value of the cash flow charged by the service agency and the valuation formula of the single mortgage.We give some numerical examples to study how parameters affect the valuation.Third,we consider the valuation problem of a residential mortgage loan with complete prepayment and default risks using a reduced form model with regime switching.Hazard rates of prepayment and default are specified as linear functions of the risk-free interest rate and house prices,which are characterized by different Ornstein-Uhlenbeck processes with regime switching.To obtain the explicit expression of the valuation,we derive the distribution of transition times for continuous time two-state Markov chain in a finite time interval and the conditional joint probability density function of transition number using the uniformization technique.Besides,we analyse the impact of parameters on the valuation of mortgage.