A General Approach for Pricing Rollover Options

Abstract

When an insurance company sells a mutual fund with death and maturity guarantees to its client, it may consider allowing the client to extend the guarantee for some more years. If the renewal only happens once, a so-called rollover option is implied in the contract. In this paper, we show how the generalized Bermudan option can be applied to the special case of the rollover option. By avoiding the heavy mathematical tools which are necessary to prove the existence of a hedging strategy, we will focus on the calculations that are common in the Black-Scholestype analysis. Contrary to Bilodeau (1997) who analyzed the one-time renewal, we can refer to the results on the (generalized) Bermudan option for which the existence of a hedging strategy was already proved. We will see that the strike price has to be adjusted if the contract is renewed in order to explicitly calculate the price of the contract.