Valuation of n-fold compound barrier options with stochastic interest rates

This paper considers the pricing of n-fold compound options with barriers. It can apply to financial derivatives with credit risk and real option applications with the right to abandon prior to maturity based on compound option theory. According to the correlation between barriers in intervals, there are two cases. One is the case of independent barriers, since the underlying value has uncorrelated default boundaries during different time intervals, while the other has correlation and results in a loosened default barrier stage by stage. Additionally, we develop a generalization of compound barrier options with stochastic interest rates to capture the interest rate risk. Finally, the characteristics of the model are illustrated with numerical examples. We find the following three results. First, the down-and-out barrier brings an early termination premium if the option is likely to be out-of-the-money in the future. Second, the loosened barrier in the case of dependent barriers has less probability of being knocked out as soon as passing through an earlier passage time. Third, a compound option with a barrier is more difficult to hedge, while increasing the number of folds reduces this difficulty.