Using the Black–Derman–Toy interest rate model for portfolio optimization

No-arbitrage interest rate models are designed to be consistent with the current term structure of interest rates. The diffusion of the interest rates is often approximated with a tree, in which the scenario-dependent fair price of any security is calculated as the present value of the risk-neutral expectation by backward induction. To use this tree in a portfolio optimization context it is necessary to account for the so-called “market price of risk”. In this paper we present a method to change the conditional probabilities in the Black–Derman–Toy model to the physical (or real) measure, including the market price of risk, and explore the economic implications for expected spot rates and for expected bond returns.