Generalized Ho-Lee Model

Abstract

This article presents a multifactor arbitrage-free interest rate lattice model. The model uses a state and time dependent implied volatility function. In calibrating this function from the set of swaption prices over a range of tenors and expiration, the interest rate model can capture surface not just the perceived volatility but the distributional form, in terms of the mix of lognormal and normal distributions, and the correlations of the rates. Swaptions are actively traded in the market that reflects the market views on the yield curve stochastic movements. Interest rate models tend to fix a distributional form or the correlation matrix of the rates, and therefore, they fail to subtract the market views from the swaption prices. This article provides a model that overcomes these crucial assumptions and it can be shown to provide significant explanatory power and computational efficiency. This model interest rate process has a number of desirable properties: (1) Consistent with historical rate experiences, with a mean reversion process, non-explosive rates, and truncated low rates. (2) A binomial recombining lattice provides efficient algorithms for American options and stratified sampling in valuing path dependent securities. (3) Straightforward to specify the multi-factor model and to specify the key rate durations and key rate vegas for risk management. The model is tested in this article empirically using monthly swaption prices over a one year sample period. The results show that the model can be calibrated to the observed swaption prices quite accurately.