• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.213-225
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• 2004

A fixed-strike lookback option is an option whose payoff is determined by the maximum (or minimum) price of the underlying asset within the option's life. Under the Black-Scholes framework, the time-t price of an equity asset follows a geometric Brownian motion. Applying the method of Esscher transforms, this paper will derive explicit pricing formulas for fixed-strike lookback call and put options, respectively. In addition, this paper will show a relationship (duality property) between the pricing formulas of the call and put options. Finally, this paper will derive explicit pricing formulas for the fixed-strike lookback options when their underlying asset pays dividends continuously at a rate proportional to its price.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.191-196
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• 2002

Sales of equity-indexed annuities (EIAs) have rapidly increased, but the growth rates in sales have recently shown signs of slowing down because the current volatile equity market increases the costs of guarantees in EIAs. New EIAs need to be designed that are similar to existing EIAs but have a cheaper guarantee and a higher participation rate. This paper proposes three types of EIAs with higher participation rates: up-and-in barrier EIA, aulual reset EIA with up-and-in barriers, and partial-time lookbackEIA. It also presents a probability distribution and the method of Esscher transforms, with which explicit pricing formulas for these EIAs are derived.