Yield curve risk management: adjusting principal component analysis for model errors

Alternative models for hedging yield curve risk: An empirical comparison

“…As in Carcano (2009), we assume that the error terms e of two zero rates of different maturity are independent from each other. Additionally, we assume that the error term of the zero rate of maturity D k is independent from the fitted values P 3 l¼1 c ln F l t of all considered zero rates, including the zero rate of maturity D k .…”

“…The proof of the second order condition of the minimization can be obtained analogously as in Carcano (2009). For each error-adjusted hedging strategy, the optimal weights / y to be invested in each future have been calculated based on the last set of equations.…”

“…This was the case of the volatility-and covariance-adjusted models tested by Carcano and Foresi (1997) and of the 2-factor PCA tested by Falkenstein and Hanweck (1997) which was found to lead to better immunization than the corresponding 3-factor PCA. Carcano (2009) tests a model of PCA-hedging which controls the exposure to model errors. He finds that -by introducing this adjustment -3-component PCA does lead to better hedging than 2-component PCA, as theory would suggest.…”