The influence of a stochastic interest rate on the n-fold compound option

We reintroduced the idea of an n-fold compound option as a generalization of Geske’s (2- fold) compound option in the same framework of constant interest rates. For the valuation of long-term financial agreements (life insurance products) this assumption is not always realistic. So that the stochastic modelling of the interest rates might be a better approach. According to Miltersen et al., we will use the requirement of simple interest rates over a fixed finite period to be log-normal distributed, instead of the continuously compounded interest rates. With these assumptions, closed-form solutions are determined for the n-fold compound call options written on zero-coupon bonds.