Interest Rate Hedging for Doubly Stochastic Markov Chains in Life Insurance

Specialeforsvar: Adam Lindholm Lenzing

Titel: Interest Rate Hedging for Doubly Stochastic Markov Chains in Life Insurance

Abstract:  The level of interest rates play a crucial role within life insurance. Even minor movements in interest rates can have a large impact upon insurance companies’ liabilities, especially if no interest rate hedging is performed. In this thesis, we present a way of hedging interest rate risk upon the liabilities within an extremely general life insurance model. We implement sophisticated financial derivatives and apply them as practitioners do. Financial mathematics and instruments are studied in detail with the purpose of hedging interest rate risk. We show and utilize the existence of a closed-form solution to the price of a
swaption when the short rate follows a one-factor model. We incorporate a stochastic and dependent financial market to a life insurance contract by constructing a doubly stochastic Markov chain for the states of the insured. One of the main and new contributions of this thesis, is that we prove the reserve satisfy a partial differential equation which generalizes many of the usual models considered in life insurance. Furthermore, we show how the partial differential equation simplifies to an ordinary differential equation when certain affine assumptions are made. In a numerical study, we show how to compute the reserve by solving the partial differential equation and how to perform an interest rate hedging strategy in practice. Finally, we demonstrate, how applying swaptions to the hedging strategy greatly increases the performance of neutralizing the level of interest rates on the reserve.

Vejleder:  Jesper Lund Pedersen
Censor:    Lars Frederik Brandt Henriksen, PFA