Journal of Risk

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

Chung-Jui Wang, Stan Uryasev

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 cashflows, lenders must maintain a balance between expected revenue and risk. We employ a conditional value-at-risk (CVaR) risk measure in this efficient execution model that maximizes expected revenue under a CVaR 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 the CPLEX-90 solver on a PC.

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