Computing Arbitrage-Free Yields in Multi-Factor Gaussian Shadow-Rate Term Structure Models

Arbitrage Restrictions and Multi-factor Models of the Term Structure of Interest Rates. 1 Arbitrage Restrictions and Multi-factor Models

In this paper we investigate models of the term structure where the factors are interest rates. As an example, we derive a no-arbitrage model of the term structure in which any two futures (as opposed to forward) rates act as factors. The term structure shifts and tilts as the factor rates vary. The cross-sectional properties of the model derive from the solution of a twodimensional autoregress...

Complete Characterisation of Arbitrage Free Affine Term Structure Models

It is widely believed that the results in Duffie and Kan (1996) provide the necessary and sufficient conditions for a multifactor model of the term structure of interest rates to admit an affine representation. It is shown here that, in fact, only sufficient conditions are given by Duffie and Kan, and there are families of affine models that do not fall into the Duffie-Kan characterisation. A m...

Review of Continuous-Time Term-Structure Models Part II: Arbitrage-Free Models

Generating multi-factor arbitrage-free scenario trees with global optimization

Simulation models of economic, financial and business risk factors are widely used to assess risk exposures and support decisions. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the “curse of dimensionality”. There is, however, an important issue that is usually overlooked when one depart...

Pricing Interest Rate Exotics in Multi-Factor Gaussian Interest Rate Models

For many interest rate exotic options, for example options on the slope of the yield curve or American featured options, a one factor assumption for term structure evolution is inappropriate. These options derive their value from changes in the slope or curvature of the yield curve and hence are more realistically priced with multiple factor models. However, efficient construction of short rate...