  The Istanbul options were first introduced by Michel Jacques in 1997. These
derivatives are considered as an extension of the Asian options. In this paper,
we propose an analytical approximation formula for a geometric Istanbul call
option (GIC) under the Black-Scholes model. Our approximate pricing formula is
obtained in closed-form using a second-order Taylor expansion. We compare our
theoretical results with those of Monte-Carlo simulations using the control
variates method. Finally, we study the effects of changes in the price of the
underlying asset on the value of GIC.
