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The Istanbul options were first introduced by Michel Jacques in 1997. Thesederivatives are considered as an extension of the Asian options. In this paper,we propose an analytical approximation formula for a geometric Istanbul calloption (GIC) under the Black-Scholes model. Our approximate pricing formula isobtained in closed-form using a second-order Taylor expansion. We compare ourtheoretical results with those of Monte-Carlo simulations using the controlvariates method. Finally, we study the effects of changes in the price of theunderlying asset on the value of GIC.

A closed-form approximation for pricing geometric Istanbul options