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Mispricing of Volatility in theIndian Index Options Market

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  • Varma, Jayanth R.

Abstract

This paper examines the relationship between index futures and index options prices in India. By using futures prices, we eliminate the effect of short sale restrictions in the cash market that impede arbitrage between the cash and derivative markets. We estimate the implied (risk neutral) probability distribution of the underlying index using the Breeden-Litzenberger formula on the basis of estimated implied volatility smiles. The implied probability distribution is more highly peaked and has (with one exception) thinner tails than the normal distribution or the historical distribution. The market appears to be underestimating the probability of market movements in either direction, and thereby underpricing volatility severely. At the same time, we see some overpricing of deep-in-the-money calls and some inconclusive evidence of violation of put-call-parity. We also show that the observed prices are rather close to the average of the intrinsic value of the option and its Black-Scholes value (disregarding the smile). This is another indication of volatility underpricing.

Suggested Citation

  • Varma, Jayanth R., 2002. "Mispricing of Volatility in theIndian Index Options Market," IIMA Working Papers WP2002-04-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    • Handle: RePEc:iim:iimawp:wp00012
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    References listed on IDEAS

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    1. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    2. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    3. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    4. Varma, Jayanth R., 1999. "Value at Risk Models in the Indian Stock Market," IIMA Working Papers WP1999-07-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
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    Cited by:

    1. Sonali Jain & Jayanth R. Varma & Sobhesh Kumar Agarwalla, 2019. "Indian equity options: Smile, risk premiums, and efficiency," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 150-163, February.
    2. Narain & Narander Kumar Nigam & Piyush Pandey, 2016. "Behaviour and determinants of implied volatility in Indian market," Journal of Advances in Management Research, Emerald Group Publishing Limited, vol. 13(3), pages 271-291, November.

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