Stochastic programming for funding mortgage pools

Abstract

We present how to use stochastic programming to best fund a pool of similar fixed-rate mortgages through issuing bonds, callable and non-callable, of various maturities. We discuss the estimation of expected net present value and (downside) risk for different funding instruments using Monte Carlo simulation techniques, and the optimization of the funding using single- and multi-stage stochastic programming. Using realistic data we computed efficient frontiers of expected net present value versus downside risk for the single- and the multi-stage model, and studied the underlying funding strategies. Constraining the duration and convexity of the mortgage pool and the funding portfolios to match at any decision point, we computed duration and convexity hedged funding strategies and compared them with those from the multi-stage stochastic programming model without duration and convexity constraints. The out-of-sample results for the different data assumptions demonstrate that multi-stage stochastic programming yields significantly larger net present values at the same or at a lower level of risk compared with single-stage optimization and with duration and convexity hedging. We found that the funding strategies obtained from the multi-stage model differed significantly from those from the single-stage model and were again significantly different to funding strategies obtained from duration and convexity hedging. Using multi-stage stochastic programming for determining the best funding of mortgage pools will lead, in the average, to significantly higher profits compared with using single-stage funding strategies, or using duration and convexity hedging. An efficient method for the out-of-sample evaluation of strategies obtained from multi-stage stochastic programming models is presented.