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

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 -the Black-Scholes-Merton Option Pricing Model (BSM) and Duan"s NGARCH option pricing model -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.

Hedging strategy in emerging market: Application long straddle option in gold price index

“…The results of this study support and are in line with the results obtained by Zhang et al (2019) where the Black Scholes model gives better results than th GARCH model for the Shanghai 50ETF index. In addition, several others study also gave the same results as those examined by Jiratumpradub & Chavanasporn (2016), Bhat & Arekar (2016) and Kaminski (2013). Meanwhile, the results obtained by researcher oppose the results obtained by Narayan et al (2016) and Hendrawan (2010) where they prove that the GARCH Model and its derivatives are better than the Black Scholes model for each research object.…”

“…The results stated that modeling an option contract with the Black Scholes model resulted in a lower AMSE value than GARCH Model. There area also several other studies comparing Black Scholes and GARCH Model that have been studied by Jiratumpradub & Chavanasporn (2016), Bhat & Arekar (2016), Kaminski (2013) and Hendrawan (2017 propriate for long term contracts. Not only the contract , but also the option strategy plays an important role in determining the benefits.…”

Tackling Investment Risks Using Equity Options During Extreme Economic Upheavals: Indian Evidence

“…Srivastava (2003) has also documented the expiration effect of the options contracts. If the options contracts violate arbitrage bounds, it shows that the options are priced against general properties of options pricing models (Bhat & Arekar, 2016;Jiang & Tian, 2011). No upper arbitrage boundary violations are seen in the Indian options market.…”

“…Moreover, a selection on the type of options for effecting the hedge is contingent upon the trade-off between the risk perception of the investors and their willingness to have initial financial outlay (Ederington, 1979;Bond & Thompson, 1985). The ATM options are likely to deliver accurate expectancy on the actual value of the underlying asset (Srivastava & Shastri, 2020) with relatively lesser prices compared with other moneyness levels due to the lower level of implied volatility (Bhat & Arekar, 2016) and they can be selected by those who neither expect further massive changes in the existing value of the underlying asset nor wish to pay more for securing their interests. If they intend to secure probable purchases of equity, holding call options at a ratio of 1.09, i.e., slightly higher than the naïve position, may provide an assured risk reduction up to 91.12%.…”

Is Indian Equity Options Market Suitable for Hedging When the Options Payoff Structure Changes?

“…where , and , are the contemporaneous implied index level of call options or put options and actual index level at time , respectively, ̂0 and ̂1 are parameters and ̂, is the error that represents the deviation from the equilibrium. Further, Following Kim, Kim, and Nam (2009), vector error correction models are used in the study to estimate the short run association between the markets using equation (9) and (10).…”