I downloaded data from NSE(National Stock Exchange) website regarding closing price of European Call Option written on Index. From standard textbook, I read that option contract must satisfy $C(t) \geq S(t)e^{-dt} - Ke^{-rt}$ where S(t) is the value of underlying Security, d is the dividend rate, r is risk free rate of interest, k is strike price, and t is time to maturity.

When I calculated minimum price, i found many contract were priced less than their minimum price. Not only these, such contract were evenly distributed across various maturities so not restricted to just near the maturity , say less than one week. Further not only highly deep in the money contract but many contract near the money found below their minimum price.

I read in book, if option traded at below minimum price it would lead to arbitrage opportunity. I want to know why these contracts price below their minimum price?

To calculate Minimum price, I used following methodology : 1) Option contract having volume less than 500 is excluded. So only actively traded option contracts are considered. 2) Risk free rate of interest is proxy by treasury rate.

Your answer will be appreciated. Thanks.

  • $\begingroup$ Could you point us to the data of such an option? $\endgroup$ – Bob Jansen Jul 28 '15 at 9:07
  • $\begingroup$ I download data period from 1-04-2009 to 31-03-2015 from NSE website on European Call Index Option written on CNX Nifty. $\endgroup$ – Neeraj Jul 28 '15 at 10:45
  • $\begingroup$ It'd be good if you can actually give a link so that we don't have to do the search and give a simple example. In any case, your pricing model might not match. Are you even sure the risk-free rate is the treasury rate? $\endgroup$ – HelloWorld Jul 28 '15 at 11:57
  • $\begingroup$ yes i used treasury rate $\endgroup$ – Neeraj Jul 28 '15 at 12:53
  • $\begingroup$ Check two things: 1 Are you using correct risk free rate? Should be something like 7 or 8%. 2 f&o Bhav file does not provide you with bid and ask prices, only settlement prices. It is possible that settlement price for some options is below arb because bid ask is wide, and average (or settlement from last price - stale) is meaningless. Finally I suggest you add one example to your question - all the numbers, rates and prices. $\endgroup$ – onlyvix.blogspot.com Jul 29 '15 at 15:26

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