Pricing Rate of Return Guarantees in Regular Premium Unit Linked Insurance

We derive general pricing formulas for Rate of Return Guarantees in Regular Premium Unit Linked Insurance under stochastic interest rates. Our main contribution focusses on the effect of stochastic interest rates. First, we show the effect of stochastic interest rates can be interpreted as, what is known in the financial community as, a convexity correction. Second we link the LIBOR Market Model to our model of the economy. This allows us to find guarantee prices consistent with observed cap and swaption prices. Numerical results show the effect of this more sophisticated interest rate modelling is considerable. We also consider ways of approximating Asian option values through tight bounds. We show that we can obtain accurate bounds in spite of the high volatility induced by the long maturities of the guarantees