An effective hybrid variance reduction method for pricing the Asian options and its variants

Lu, King-Jeng; Liang, Chiung‐Ju; Hsieh, Ming‐Hua; Lee, Yi-Hsi

doi:10.1016/j.najef.2019.04.004

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2020

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“…If we consider a Black and Scholes (1973) model, the valuation of products such as the arithmetic Asian options (AAOs) becomes very difficult since the hypothesis of taking the underlying asset price is a geometric Brownian motion does not allow to obtain a closed-form pricing formula because the distribution of the sum of log-normal random variables is not known in theory. However, the price of AAO can be approximated in practice by Monte-Carlo (MC) simulations with variance reduction techniques (see Zhang (2009), Mehrdoust (2015) and Lu et al (2019)). It is also possible to approach the price of AAO with a Taylor expansion as in Ju (2014).…”

Section: Introductionmentioning

confidence: 99%

A closed-form approximation for pricing geometric Istanbul options

Kacef

Boukhetala

2020

IJRM

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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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