ABSTRACT
Interest-rate models are necessary for pricing most interest-rate derivatives and for gauging the risk of general interest-rate instruments. Equilibrium models may have a sound financial economical background, but they do not automatically reproduce the market price of benchmark bonds, or reproduce the yield curve, unless a calibration procedure has been carried through. With historical data of US Treasury yields, we demonstrate the estimation of model parameters of the Heath–Jarrow–Morton (HJM) model, using an important technique called principal component analysis. The HJM model lays down the foundation of arbitrage pricing in the context of fixed-income derivatives, and it is considered a milestone of financial derivative theory. Arbitrage pricing models have been generated from the HJM framework by making various specifications of forward-rate volatility. The arbitrage pricing models are rooted in the efficient market hypothesis, which states that market prices of instruments do not induce any arbitrage opportunity.
