Planning Your Own Debt; a Stochastic Programming Approach to Mortgage Backed Security Analysis in a Two-Factor Interest Rate Model

Abstract

In Denmark many homeowners/borrowers manage their debt very actively. The individual borrower faces a number of non-trivial decisions. He has to decide whether to use adjustable rate loans where the debt is refinanced on a yearly basis or the more traditional fixed rate 20- or 30-year annuities (or some combination). The annuities have embedded options; first there is a call-feature, second there is a delivery option. We use a stochastic two-factor term structure model (calibrated to market prices and volatilities of non-callable bond and prices of callable bonds) and formulate the problem of optimal (with respect to some concave criterion) debt management (subject to investor specific conditions) as a multistage stochastic programming problem that can be solved with standard software. The formulation makes it easy to incorporate both the inherently path-dependent aspects and the optimal policy aspects. Preliminary results indicate that the advice/"rules of thumb" used by banks/financial institutions are reasonable, albeit best suited for more aggressive (or large) investors, for whom the delivery option is of some value, while it appears that suitably calibrated one-factor models may produce results similar to the two-factor model.