The Effective Duration and Convexity of Liabilities for Property-Liability Insurers Under Stochastic Interest Rates

Managing interest rate risk for property-liability insurers requires appropriate measurement of the sensitivity of liabilities to movements in interest rates. Most prior studies have assumed that interest rates shift in a parallel fashion and that the cash flows from liabilities are unaffected by interest rate changes. This article recognizes that unpaid property-liability (P-L) insurance losses are inflation-sensitive, that movements in interest rates will affect future claim payouts due to the correlation between interest rates and inflation and that interest rates are stochastic. The effective duration and convexity of P-L insurance liabilities calculated based on this approach are substantially lower than those measured using traditional approaches, which has important implications for asset-liability management by P-L insurers. Keywords: duration, term structure model, property-liability insurance