Evaluation of Insurance Products with Guarantee in Incomplete Markets
Abstract Life insurance products are usually equipped with minimum guarantee and bonus provision options. The pricing of such claims is of vital importance for the insurance industry. Risk management, strategic asset allocation, and product design depend on the correct evaluation of the written options. Also regulators are interested in such issues since they have to be aware of the possible scenarios that the overall industry will face. Pricing techniques based on the Black & Scholes paradigm are often used, however, the hypotheses underneath this model are rarely met. To overcome Black & Scholes limitations, we develop a stochastic programming model to determine the fair price of the mini…
Pricing the Option to Surrender in Incomplete Markets
New international accounting standards require insurers to reflect the value of embedded options and guarantees in their products. Pricing techniques based on the Black and Scholes paradigm are often used; however, the hypotheses underneath this model are rarely met. We propose a framework that encompasses the most known sources of incompleteness. We show that the surrender option, joined with a wide range of claims embedded in insurance contracts, can be priced through our tool, and deliver hedging portfolios to mitigate the risk arising from their positions. We provide extensive empirical analysis to highlight the effect of incompleteness on the fair value of the option.
Pricing Reinsurance Contracts
Pricing and hedging insurance contracts is hard to perform if we subscribe to the hypotheses of the celebrated Black and Scholes model. Incomplete market models allow for the relaxation of hypotheses that are unrealistic for insurance and reinsurance contracts. One such assumption is the tradeability of the underlying asset. To overcome this drawback, we propose in this chapter a stochastic programming model leading to a superhedging portfolio whose final value is at least equal to the insurance final liability. A simple model extension, furthermore, is shown to be sufficient to determine an optimal reinsurance protection for the insurer: we propose a conditional value at risk (VaR) model p…