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# Volatility Purchase

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Dear John,

Today, Todd brought to our attention someone making a large subject (a customer bought QQQ January 39 calls of 2006 and bought January 35 puts of 2006 in equal amounts)purchase. He mentioned "locking in volatility".

How does a change in volatility make this position profitable?

At the close:

QQQ closed at 37.25
Total per strangle: 8.4

By my calculations, the customer needs a 22% upside move or a 35% drop on the QQQ index by expiration to break even on this trade (my guess is the bet is to the upside).

Thank you

First of all, my calculations show that if the customer did nothing, she would break even on the trade if the QQQ index declines by 29% or if it rises by 26% by expiration (try your calculations again).

But if the customer was doing this trade for a directional bet, this trade is a very inefficient way to accomplish that: long term options have such a high notional price that is better to buy shorter term options when making a directional bet.

It is much more likely, as Todd pointed out, that the customer is making a bet that the overall level of volatility will increase. Long term options are very sensitive to changes in volatility, as reflected in the "implied volatility" used in calculating the option price. This sensitivity is measured by something called "vega": for a 1% increase in the level of volatility, an option price will move a certain amount. The "vega" of options increases with the length of time to expiration.

If the purchase was made one up, that is they bought (for every) 1000 1/39/06 calls at \$4.8 and 1000 1/35/06 puts at \$3.6, the delta (long or short) is a net positive 21 (1000 x .21 x 100) = 21,000 QQQ shares. So from a directional basis initially the straddle will act like being long 21,000 QQQ shares. I would guess, however, that the customer sold 21,000 QQQ shares against this position to make it "neutral". As the index moves higher, the delta will increase and as it moves lower it will decrease. This is called long convexity where the "gamma" (change in delta) is positive: as the index rises, the delta becomes more positive and as it declines the delta becomes more negative. The customer, trying to isolate the volatility portion of the trade, will most likely remain neutral by selling QQQ shares as the index rises and buying them back as the index declines. Notice the trader wants the index to move a lot so that those buys and sells make more money. The trader wants the index to be volatile. So much for delta.

So the real reason that the customer bought the straddle is it that she thought that implied volatility of the options is low and that it will go higher. The implied volatility of the calls is 23.8% (implying a 23.8% move in the index over one year's time) and that of the puts is 25.59%. The "vega" can be calculated so that for every 1% increase (23.8% to 24.8%) on the calls and puts, the value of the straddle will increase by around .40 = \$40,000 per 1000 straddles.

In conclusion I do not believe that this is a directional bet because directional bets are not efficiently made with long term options: a change in volatility would overwhelm the delta.

It is, however, as Todd said, a way to buy the current level of option prices (implied volatility), making a bet that volatility will increase over the next several months.

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