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An Application of GARCH Models in Detecting Systematic Bias in Options Pricing and Determining Arbitrage in Options

11 Pages Posted: 10 Mar 2012 Last revised: 31 Oct 2012

Mihir Dash

Alliance University - School of Business

Jay H. Dagha

affiliation not provided to SSRN

Pooja Sharma

affiliation not provided to SSRN

Rashmi Singhal

affiliation not provided to SSRN

Date Written: March 8, 2012

Abstract

Derivatives have become widely accepted as tools for hedging and risk-management, as well as speculation to some extent. A more recent trend has been gaining ground, namely, arbitrage in derivatives.

The critical parameter in derivatives pricing is the volatility of the underlying asset. Exchanges often overestimate volatility in order to cover any sudden changes in market behavior, leading to systematic overpricing of derivatives. Accurate forecasting of volatility would expose systematic overpricing. Unfortunately, volatility is not an easy phenomenon to predict or forecast. One class of models that have proved successful in forecasting volatility in many situations is the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family of models.

The objective of the present study is to analyze systematic bias in the pricing of options derivatives. In order to perform the analysis, data were collected for a sample of stock options traded on the National Stock Exchange (NSE) of India and their underlying stocks. In the study, GARCH models are used to forecast underlying stock volatility, and the forecasted volatility is used in the Black-Scholes model in order to determine whether the corresponding options were fairly priced. Any systematic bias in options pricing would provide evidence for arbitrage opportunities.

Keywords: derivatives, hedging, speculation, arbitrage, volatility, overpricing, GARCH, Black-Scholes model

JEL Classification: G13

Suggested Citation

Dash, Mihir and Dagha, Jay H. and Sharma, Pooja and Singhal, Rashmi, An Application of GARCH Models in Detecting Systematic Bias in Options Pricing and Determining Arbitrage in Options (March 8, 2012). Journal of CENTRUM Cathedra: The Business and Economics Research Journal, Vol. 5, Issue 1, pp. 91-101, 2012. Available at SSRN: https://ssrn.com/abstract=2018422

Mihir Dash (Contact Author)

Alliance University - School of Business ( email )

Chikkahagade Cross,
Chandapura-Anekal Road, Anekal
Bangalore, Karnataka 562106
India
9945182465 (Phone)

Jay H. Dagha

affiliation not provided to SSRN ( email )

Pooja Sharma

affiliation not provided to SSRN ( email )

Rashmi Singhal

affiliation not provided to SSRN ( email )

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