Abstract

Equity-Indexed Annuity products (EIAs) are becoming increasingly popular as they are tax-deferred accumulation vehicles that offer participation in the equity market growth while keeping the initial capital protected. This thesis focuses in particular on a special type of EIAs; the Compound Ratchet (CR). Sellers of this product, such as insurance companies and banks, retain the right to change one of the pricing parameters on each contract anniversary date, while promising not to cross a certain predetermined threshold. Changing these parameters can sometimes have an impact on the value of the EIA, which makes them interesting to study, especially when the issuer's changing policy is not clear. In order to reproduce the pattern of these changing parameters, a new approach of dynamically hedging the CR EIA and simultaneously protecting the issuer from hedging risk is proposed and tested.

Assuming the Black-Scholes Financial framework and in the absence of mortality risk, closed-form solutions for the price and value of the CR EIA at any time throughout the contract term are obtained and then used to find the Greeks, which are in turn used build the hedging strategies. In reality, trading can only be done in discrete time, which produces hedging errors. A detailed numerical example shows that the Gamma-hedging strategy outperforms the Delta-hedging strategy by reducing the magnitude of these errors. However hedging risk still exists, therefore, the new approach is applied to transfer the errors from the issuer to the buyer by dynamically changing the pricing parameters. Additionally in the numerical example, the distribution of these parameters is extracted and analyzed, as well as the resulting reduction in the hedging errors, which represent the reduced cost for the issuer.