Natural Hedging with Fix and Floating Strike Guarantees

Abstract

The paper analyzes minimum return rate guarantees (MRRGs) including fixed guarantee rates prevailing for the whole contract horizon as well as floating guarantee rates which are linked to the interest rate evolution. In a complete arbitrage free market where the asset and bond price dynamics are given by Gaussian processes, we obtain closed form pricing solutions for both guarantee schemes. Differences in the guarantee costs are then explained by the difference of the arbitrage free values of the fix and floating rate guarantees and the difference between cumulated volatilities resulting from forward and simple volatilities. We then consider the perspective of the asset liability management, i.e. we analyze the sensitivities of the asset and liability side against changes in the interest rate. We show that a combination of fix price and floating strike guarantees enables a natural hedge against changes in the interest rate.