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# Reminiscences of an Option Trader: Pinball Wizard

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## Do break-evens to get a feel for your risk, a risk that you are willing to live with.

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Tommy Carden, a great trader friend of mine, called me yesterday before Google (GOOG) earnings and asked my opinion of a trade: short 100,000 shares at \$425 and sell 2000 February 380 puts at \$9.10. He wanted to assign a .50 delta to this trade, far from the theoretical delta produced by common option models.

The theoretical delta on these puts at the time was only .20. The delta is the probability that the stock will be at or below the strike of 380 by expiration; the delta indicates that the price of the put will increase by \$.20 for every \$1 the stock drops (or decrease by \$.20 as the stock rises \$1). It is clear from the "models" that if he sold that much stock against his short puts he would lose more money on the way up and make more on the way down than a "delta neutral hedger" using the theoretical delta of .20.

The delta changes dynamically in a non-linear way: the delta increases at an increasing rate as the stock drops (as does the probability that the stock will be at the strike) until it gets to 1 by going in the money at expiration. This is what we mean when we talk about convexity: the delta changes exponentially (the graph of the change is a parabola).

The delta also depends on the volatility: the more volatile a stock, the higher the probability that it can drop below a strike so far away. Thus, the higher the implied volatility (the more expensive) of an option, the higher the delta will be for an out-of-the-money strike. If the option had been much cheaper (the implied volatility much lower, implying a much less volatile stock), the delta would have been much less. If one said that GOOG is not really that volatile a stock, one would think those puts worthless and had very little delta. Such a person would sell those puts with no or little short stock to hedge it.

My friend is not such a person. He took the opposite view. He did not realize it consciously, but he was implying through the higher delta he was assigning to the trade that he fully believed that the stock could move to that extreme on the downside and thus the options deserved a higher delta than the one produced by the option price (implied volatility). In sum, he thought the put was cheap, not expensive. So if he thought that the option was cheap and that the delta was low, why did he sell it?

He sold the option because of his intuition of how the options would react if the stock went up instead of down. He sold the option because he built in his mind a distribution of stock prices that he believes actually exists. He sold the option because option prices and theoretical deltas are all based on a normal distribution of stock prices: that they can go up and down with equal probability at equal rates. He thinks this is false: that at this point, based on his custom built distribution of stock prices, he believes that the stock can go down much faster and to a greater degree that it can go up.

In other words, I take back what I originally said about him believing that the option was cheap. It is true that the delta is smaller for an out of the money option the lower the volatility, but there is another reason why he can disagree with the delta and still think the option is expensive. Tommy understands intuitively that options are not priced correctly, that option models assume a normal distribution of stock prices, that they assume skinny tail probabilities, and because of that, they throw off incorrect details like deltas.

We of course did not talk about any of that. In typical trader code, we communicated all that was necessary in a few seconds and words. He showed me the trade and I simply said at that delta the break-evens are \$317 and \$443 and if you are willing to be long or short at those prices in the amount equal to 100,000 shares then do the trade (the break-evens at the theoretical delta were \$ 357 and \$ 470, but importantly long 160,000 shares at the low or short 40,000 shares at the high).

The Pin Ball Wizard is blind, but somehow feels his way to a score. What I wanted to point out in this rambling and obtuse discussion, and what I hope you get out of it, is that options are not a science, that theoretical deltas and gammas are at best a guess. The main reason for that is that option models are based on linear math such as bell-shaped normal distributions, implying that the world is cozy and definable, and which are not realistic. The world is much messier than that and intuition does just as much to describe it as anything.

Understand option theoreticals to the point of dismissing them (understanding things like how delta responds to increases or decreases in volatility changes is something I learned from practice and I now treat it like breathing). Do break-evens to get a feel for your risk, a risk that you are willing to live with.

Tommy did the trade and made more money than someone who did it "delta neutral."
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