Communications in Mathematical Finance

Moment-matching technique and General mean model in pricing Lookback option

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  • Abstract

    In option pricing one of the main problems to solve is how to determine the fair price of an option when no-arbitrage opportunity is considered. To solve this problem many models have been developed but most of them there is no closed form solutions. In this paper, general mean model is used to price Lookback option since it can entervene in determination of minimum and maximum of underlying asset price under some conditions. The study shows the construction of lattice using moment-matching which provide a system of linear equations where real world probabilities are unknown. To solve this system, Vandermonde matrix is preferred as one of the easiest way to use. Since it is not allowed to price with real world probabilities and as this paper deals with incomplete market which has more than one martingale measure, it is needed to choose the best one to use in pricing. Therefore, the relative entropy method is introduced to find the minimum entropy martingale measure which is the neutral probability in other words. Finally, the results from pricing Binomial floating lookback option is compared to well known Black-Scholes model. 

    Keywords: Lookback option; Incomplete market; moment-matching; general mean; relative entropy martingale measure; Vandermonde matrix; Binomial model; Black-Scholes model