A closed-form approximation for pricing geometric Istanbul options

The concept of Istanbul options were first introduced by Michel Jacques in 1997. These derivatives products 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 standard 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. We also carry out a comparative price study with an arithmetic Istanbul call option. Finally, we study the effects of changes in the price of the underlying asset on the value of GIC.