Arbitrage-Free Modeling of the Term Structure of Interest Rates (in Danish)

Abstract

Initially we set up the new framework developed by Heath, Jarrow and Morton (1987) and specifies the process for bond-prices, spot-rates and forward-rates assuming a deterministic volatility structure. However, the main contribution of this paper is in determining the bridge between this new modelling framework and the traditional yield-curve modelling approach.In that connection we consider the following one-factor models: Cox, Ingersoll and Ross (1985), Vasicek (1977) and Longstaff (1989). With respect to two-factor models we analyse the following 2 models: Longstaff and Schwartz (1991) and Vasicek and Fong (1991). Lastly, we also consider the general multi-factor gaussian yield-curve model from Langetieg (1980). With respect to these models we derive the embedded volatility structure and relate them to the HJM modelling framework.Next, using the Hull og White (1990b)/(1993) model, it is shown that when introducing a time-dependent parameter in the drift-specification and in the volatility-specification that it is possible to match both the initial yield-curve and the initial volatility structure - this derivation is performed using the HJM framework.Lastly, multiple candidate trinomial models is being derived/analysed for the Hull and White model.