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Penny Stocks 2013

Penny Stocks 2013

How do I caluclate the price of a put option?

On March 8th 2013, the closing price of Target stock was $66.35. A call option with strike price X = $55.00 and maturity date April 19th 2013 cost $11.30. A put option with the same strike and maturity cost $0.08. Assume an annual percentage risk-free rate of 0.00096 (0.096%). To compute the proper rate for discounting, assume exactly one month until maturity.If put-call parity holds, what should the price of the put option be?

First it is clear the call price given in the problem is incorrect. If it were correct a trader could short the stock at $66.35, buy the option for $11.30, then exercise the option to buy the stock for $55.00 giving him a risk free profit of $0.05 per share. The market is too efficient to allow a risk free profit.

The only way that price could be correct would be if (1) it was a European style option and (2) the stock went ex-dividend between March 8 and expiration. In that case the a trader who shorted the stock would be responsible for paying the $0.36 per share dividend paid on March 9. However the stock went ex-dividend February 15, so the trader would not be responsible for the dividend.

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Given an annual rate of 0.00096 you would have a monthly rate of 0.00008. That would make the future price of the stock 1.00008 x 65.35 = 65.355.

65.355 – 55 = 10.355

10.355 x 1.00008 = 10.3558 or 10.36 rounded to the nearest penny.

That would make the price of the put 10.35 – 10.36 = -$0.01. Since the price of the put cannot be negative this confirms that the price of the call given was incorrect.

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If the ex-dividend date, instead of the dividend date, had ben March 9, and the options were European style, the cost of the call option could be correct. That would make the future price of the stock 1.00008 x (65.35 – 0.36) = 64.995.

64.995 – 55 = 9.995

9.995 x 1.00008 = 9.9958 or 10.00 rounded to the nearest penny.

That would make the price of the put 10.35 – 10.00 = $0.35.

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I suspect what happened is that the values in the question were take from the “last” quotes after the market closed on March 8. However options with strike price over 15% away from the stock price one month prior to expiration may be very thinly traded, so the stock price may have changed significantly since the time these options were traded.

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