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Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

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  • Aparna Bhat
  • Kirti Arekar

Abstract

Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models ¨C the Black-Scholes-Merton Option Pricing Model (BSM) and Duan¡¯s NGARCH option pricing model ¨C for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the ¡®volatility smile¡¯. This bias of the BSM results from its assumption of a constant volatility over the option¡¯s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

Suggested Citation

  • Aparna Bhat & Kirti Arekar, 2016. "Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 8(3), pages 123-136, March.
    • Handle: RePEc:ibn:ijefaa:v:8:y:2016:i:3:p:123-136
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    References listed on IDEAS

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    2. Riko Hendrawan, 2023. "Comparison of Black-Scholes and GARCH Option Models on The Jakarta Islamic Index with Collar Strategy," GATR Journals jfbr209, Global Academy of Training and Research (GATR) Enterprise.
    3. Daniel Erpriandy Maharsasi, 2022. "Testing Black Scholes and Garch Model Options on Gold Price Index With Long Strangle Strategy Using 1985-2020 Data ," GATR Journals jfbr207, Global Academy of Training and Research (GATR) Enterprise.

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    More about this item

    Keywords

    Black-Scholes-Merton; currency options; implied volatility; NGARCH; Non-Linear Least Squares;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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