Improved Hedging of interest rate volatility

This thesis examines dierent methods to determine and hedge the vega exposure of a liability portfolio with non-linear payout. The liability portfolio with non-linear payout behaves like a portfolio of interest rate derivatives. Vega exposure is the sensitivity of the portfolio value to changes in the volatility of interest rates. Valuation of the liabilities requires a term structure interest rate model. This work uses a LIBOR Market Model (LMM) with Displaced Diusion (DD) for liability valuation. The Stochastic Alpha Beta Rho (SABR) model is used for asset valuation. The starting point is the current methodology of Aegon NL, called the indirect alpha method. We analyse the indirect alpha method and expose its strengths and weaknesses. From the results of this analysis, we identify three alternative methods to determine the vega exposure: the LSRV method, the Black Implied Volatility method and the Ordinary Local Volatility method. We implement these alternatives and use a constrained least squares algorithm to determine the optimal hedge portfolio for each method. We evaluate the hedging performance of these hedges with historical scenarios, simulation and backtesting. The evaluation shows that all alternatives improve on the indirect alpha method. The statistical dierences between the alternatives are small.