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I have spoken in generalities and in graphs about volatility strategies: selling volatility by being short expensive options or buying volatility by buying options, and hedging the options against stock to be delta neutral (neutral price direction). These are strategies I use to isolate what I think are expensive or cheap options. Basically, if I buy volatility and the stock is more volatile than the options price implies or if I sell options and the stock is less volatile than the options imply, I make money. A specific example of a long volatility strategy (called a back-spread) will make this clearer.

I decide that the KLAC 10/50 options (fictitious options) are cheap relative to what I think of the actual future volatility of the stock. The options price of \$4.19 with the stock at \$49.50 implies a volatility of 42% (expect the stock to be up or down 42% in one year). This means on a daily basis the stock should trade in a 2.65% range (42% divided by the square root of 250 trading days). Let's analyze the actual daily profits and losses of the position assuming the stock is more volatile than the options imply (the scenario where I should make money):

I initiate the position neutral: short 53,000 shares against 1,000 long calls because at the outset, the options will move \$.53 for every \$1 move in the stock (delta). On the first day the stock goes up by 4%, more than that which is implied by the option, to \$51.50, an actual volatility of 63%. Because of the rise in the stock, the delta (the probability that the stock will be in the money by expiration) increases by the amount of the gamma (the second derivative of price; the amount that the delta will move relative to the stock price) from .53 to .60. So at the end of the day we are long 60,000 shares (1000 x 100 x .6) through the options and short only 53,000 actual shares; to remain neutral I sell 7,000 shares at \$51.50. There is a mark to mark profit of \$5,000 because the stock moved up more than the price of the option implied (the option is marked at a constant 42% volatility). The time decay is incorporated in the option price; the only cash flow that is not included in this analysis is the rebate on the short stock, which is negligible at \$.002 per share.

The next day the stock drops by 2.9%: again it moves by more than that implied by the option price. The delta of the option drops back down to .55, so at the end of the day I am able to buy back 5,000 of the 7,000 shares sold the previous day at a better price. Again there is a mark to market profit; the profit is smaller because the move in the stock is only slightly more than the option price implies. And there is the bottom line: I am able to trade the stock more profitably than the option price implies. If the stock on the other hand begins to trade less volatile than implied by the option, my stock trading profits would be less than needed to offset the losses on the option position.

In the beginning, the movement in the option price is almost exclusively dictated by the delta (forgetting about ancillary causes such as moves in interest rates, which should be hedged away through euro strips). As time goes on, the theta (time decay) will increase exponentially, but then so will the gamma (the delta will change much more for a relative move in the stock), and I will be able to trade more shares.

There are lots of ways I can subjectively change the way I re-hedge. If I feel that the stock is trending, I may only sell 5,000 shares and not 7,000 after the first day in the hope that the stock will move higher the next day. If I am wrong, it is only a slight error, but many slight errors add up to one big one. Again, option trading is both art and science.

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No positions in stocks mentioned.

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