Index Clause Valuation under Stochastic Inflation and Interest Rate

This work is focused on valuation of the reinsurer's share on a particular accident, stemming from the excess of loss (XL) reinsurance contract that applies to a general insurance annuity compensation, e.g., motor liability or workmen's compensation. The excess of loss (XL) reinsurance contract is an insurance contract between the insurer and reinsurer, which guarantees recovery payment to the insurance company for each accident in the amount of the accident that the insurance company pays off in excess of a contracted priority. Special focus is set on the impact of the so called index clause which is usually included to the reinsurance contract. The index clause allows the reinsurer to increase the originally agreed priority by a coefficient which is, roughly said, calculated as a ratio of the sum of all nominal payments to the sum of all deflated payments. Analytic valuation formula does not exist for the reinsurer's share without the index clause. Hence simulation model is used to perform the study. We assume a geometric Brownian motion for the inflation index and an Ornstein-Uhlenbeck process for the discount rate, where we allow the two processes to be correlated.