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by codeismightier
3835 days ago
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Not quite -- this guy didn't naked short a put option on Maya crude. The plan was to dynamically hedge the position -- putting on a trading strategy that continuously neutralized the first partial derivative of the payoff function. The problem was the the second partial derivative was left unhedged -- oops! To put it technically, he was delta hedged but not vega hedged. Thus when volatility spiked he lost money. Even worse, he insured 2/3 of Mexico's entire production, so when things got bad there wasn't even enough liquidity to maintain the delta hedge. A better plan would be to come up with some sort of vega hedge using WTI volatility. WTI vol and Maya vol are correlated so some sort of partial hedge should have been possible, but it's very tricky. This is why other banks were not interested. It sounded like he was either too lazy or arrogant to believe he need to vega hedge and it blew up in his face. |
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Delta, the first partial derivative on price of the Black-Scholes model of option pricing [1], is the rate at which the price of an option changes in relation to the price of the underlying asset. For example, a call option with delta=0.25 requires one own 1 unit of the underlying for every 4 options (keeping things simple) to be perfectly hedged, i.e. indifferent to changes in the price of the underlying. If you are running a leveraged operation, delta-hedged means well-hedged.
Unfortunately, as the price of the underlying changes delta changes. Yes, one can describe this relationship in terms of volatility (as the price changes, volatility will spike, which in turn feeds into the value of delta). But it is simpler to describe it in terms of the second partial derivative on price, gamma. Gamma is the rate at which delta changes in respect of price.
Non-derivative assets are delta=1 assets; for every dollar change in the price of AAPL the price of AAPL changes one dollar. Duh. Buying and selling delta=1 products helps one hedge delta. Gamma, being a second derivative, is non-linear. That means only non-linear products will aid you in your game against it. Options, and option-like products, are really the only ones with "gammaness".
Big operations gamma hedge as much as they can while trying to keep their delta contained. For example, if you sell 100 puts, you would keep yourself delta-hedged while you try to profitably buy 100 puts. Provided the price doesn't wiggle around too much, this works.
This strategy is problematic, however, if your counterparty is Mexico. Mexico wants LOTS of options. If you can't give Mexico LOTS of options, Mexico can't bother dealing with you. So you tend to want to provide Mexico with LOTS of options because LOTS of options commonly means LOTS of profits (and LOTS of fees).
But the market doesn't have a bunch of people buying and selling LOTS of options. Just lots of options. So whereas one might usually be 20 or 50 or 70 percent gamma-hedged, when one just booked LOTS of options, 2% seems like a pretty good rate for the first week after the sale. Sucks to be you if Libya or Iran or the Sauds decide crash the party in that time.
[1] https://en.wikipedia.org/wiki/Black–Scholes_model