Multifactor Interest Rate Models in Low-Rate Environments

Abstract

This thesis studies a multi-factor Heath-Jarrow-Morton model and a LIBOR mar- ket model on the Norwegian, European and US interest rate market. The main concerns are the low-rate environment and exposure to negative interest rates in these models. We begin by introducing financial markets and the mathematical models explaining them. Further we discuss the problem with the current low-rate environment and the historical market practice. The focuses are implementations of two multi-factor interest rate models and the presence of negative interest rates. The historical data is provided by DNB and consists of zero coupon swap rates for several maturities in the period 2000-2012. The volatility factors are derived from historical data using principal component analysis and covariance matrices. With today?s yield curve the probability of negative rates is highly significant in the HJM model, whereas it is zero in LMM because of lognormality. Monte Carlo is used on the models to compare prices of caps and floors. We show that the models do not produce the same price especially around strikes near the current 3-month rates. Further we price long butterfly spreads to show the absence of arbitrage in both models.