Efficient execution in the secondary mortgage market: a stochastic optimization model using CVaR constraints

Abstract

Efficient execution is a significant task faced by mortgage bankers attempting to profit from the secondary market. The challenge of efficient execution is to sell or securitize a large number of heterogeneous mortgages in the secondary market in order to maximize expected revenue under a risk tolerance. This paper develops a stochastic optimization model to perform efficient execution that considers secondary marketing functionality including loan-level efficient execution, guarantee fee buy-up or buy-down, servicing retain or release, and excess servicing fee. Since efficient execution involves random cash flows, lenders must balance between expected revenue and risk. We employ a CVaR risk measure in this efficient execution model that maximizes expected revenue under a constraint. By solving the efficient execution problem under different risk tolerances specified by a CVaR constraint, an efficient frontier could be found. The model is formulated as a mixed 0-1 linear programming problem. A case study shows that realistic instances of the efficient execution problem can be solved in acceptable time (approximately one minute) with CPLEX-90 solver on a PC. CVaR