Delta Hedging for Single Premium Segregated Fund

Segregated funds are individual insurance contracts that offer growth potential of investment in underlying assets while providing a guarantee to protect part of the money invested. The guarantee can cause significant losses to the insurer which makes it essential for the insurer to hedge this risk. In this project, we discuss the hedging effectiveness of delta hedging by studying the distribution of hedging errors under different assumptions about the return on underlying assets. We consider a Geometric Brownian motion and a Regime Switching Lognormal to model equity returns and compare the hedging effectiveness when risk-free rates are constant or stochastic. Two one-factor short-rate models, the Vasicek and CIR models, are used to model the risk-free rate. We find that delta hedging is in general effective but large hedging errors can occur when the assumptions of the Black-Scholes' framework are violated.