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# Minyan Mailbag: DAL Put-Call Parity

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Hi John,

Today I closed out of a covered call position I entered into about a month ago in DAL. I bought the stock at \$6.39 and sold the calls at \$1.70. Today, I sold the stock at \$6.4 and closed the calls at \$1.30.

Anyway, I am trying to figure the volatility behind this trade. The screen that I am using is showing that the implied volatility on the puts is very high compared to actual volatility to the stock and that the implied volatility on the calls is low compared to the actual. There is a very high short interest on the stock. So, it seems that everyone and their brother are trying to short the stock in one way or another.

So, my plan today was to short the stock and sell the puts or buy the calls. This would take advantage of the high implied volatility on the puts and/or the low one on the calls. But, the plan was foiled when Ameritrade didn't have any shares to let me short....

Was my thinking at least right on this one? I am still learning.

Minyan,
Mike Smith

It was a good try, but wouldn't work. The entire reason that the puts are trading high relative to the calls is the fact that you can't borrow the stock.

In the implied volatility using the Black-Scholes model (this model must normally be adjusted for dividends, but DAL has none) calculation you input an interest rate. When stock is hard to borrow, you have to pay a rebate (normally you sell the stock short, earn interest on the cash less a fee paid to the lender of the stock; when the short interest is abnormally high, the lender can charge a fee higher than the interest rate earned) instead of get one. So the interest rate input can be negative. When you use an appropriate negative interest rate in the model you will see that the implied volatilities for both the puts and calls are around the same.

This does not mean that the puts are not actually trading high relative to the calls, it just means that the theoretical reason that they are trading higher is exactly the fact that the stock cannot be borrowed (it actually can, but you have to pay for it).

In other words, if you calculate put-call parity without using an interest rate you will find that it is much better to short a naked put than buy the stock and sell the call (these are the exact same risk-return profiles). Notice that since you want to assume this risk you do not short the stock.

For example, with the stock at \$ 6.60, the October \$5 calls are trading at \$2.20. If you buy the stock and sell the calls, it is just like selling a naked \$5 put at \$.60 (\$2.20 - (\$6.60 - \$5)). The real put is trading at \$1.00.

So if you wanted to maintain your long stock short call exposure you could have sold out your long stock, bought back the call, and shorted the put.

But you should have just done this in the first place as long as you had a margin account. You also would have put up less money as Regulation T requires only 20% of the strike less the out of the money amount.

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