Hedging beyond duration and convexity

Hedging of fixed income securities remains one of the most challenging problems faced by financial institutions. The predominantly used measures of duration and convexity do not completely capture the interest rate risks borne by the holder of these securities. Using historical data for the entire yield curve, we perform a principal components analysis and find that the first four factors capture over 99.99% of the yield curve variation. Incorporating these factors into the pricing of arbitrary fixed income securities via Monte Carlo simulation, we derive perturbation analysis (PA) estimators for the price sensitivities with respect to the factors. Computational results for mortgage-backed securities (MBS) indicate that using these sensitivity measures in hedging provides far more protection against interest risk exposure than the conventional measures of duration and convexity.