A closed-form approximation for pricing geometric Istanbul options
Mohamed Amine Kacef, Kamal Boukhetala
TL;DR
This paper introduces a closed-form analytical approximation for pricing geometric Istanbul options within the Black-Scholes framework, validated against Monte Carlo simulations and analyzing underlying asset price effects.
Contribution
It presents the first closed-form approximation formula for geometric Istanbul options, extending Asian option pricing methods.
Findings
The approximation closely matches Monte Carlo simulation results.
The formula simplifies the computation of Istanbul option prices.
Asset price changes significantly impact GIC values.
Abstract
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.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Stochastic processes and statistical mechanics
MethodsGraph InfoClust