Mispricing of Volatility in theIndian Index Options Market

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.