Dazed and Confused

A trader should NOT leave the pit. Some new hand held devices allow for quick calculations electronically, at least now. But in 1987, only small calculators were allowed in the pit. Besides, if you cannot handle being quick in the pit, being able to add, subtract, multiply and divide COLUMNS in your head, you have no business being there.

So let's summarize what we've determined from "eyeballing" the position. We've determined:
a) We are long gamma, given a one strike move either way.
b) The position is delta neutral, even when subtracting boxes.
c) The optimal overnight move up would be two strikes to the 92 strike.

And we know from experience that we can back out the approximate "expected move" in our heads.
Volatility is one standard deviation (66% probability) normalized for the number of
trading days in a year (256 vs. 365). So first we need to "annualize" it. 365/256 is roughly 1.4.
And the correct way to normalize this is to take the square root of that ratio and multiply that.
The square root of (365/256) is 1.19, a good ratio to rmember for the purposes of normalizing. So, 17% on a 256 day basis is 20% on a 365 day basis. The square root of 20% (.20) is roughly .44.

Variance (v^2) is the summation difference of a probability times all moves over a period minus the average move. And we can guessimate that to be 1/2 of the variance. We see that we can ballpark that to be 22 ticks. It is not necessary to calculate this as the vol tells us this already.

In our heads we divide 22 by 360. (Rounding off 360 ays we are de-annualizing to a daily volatility) Clearly our expected move implied by this is only 6 ticks (Or multiply 22 by .36 and then multiply by 100) So our one strike move scenario falls apart completely. We are going to get KILLED overnight as implied by this volatility.

BUT, overnight the crash circles the globe. It was apparent that a flight to quality in US based securities would be imminent. Moreover, in a flight to quality scenarion, not only would the long end rates plummet, but the TED would widen considerably, as T bills have better "quality" than Euros. But as I trader, I didn't have a fricking clue what was going to happen.

So now, let's return to market conditions the night after the close of Black Monday. It was nearly impossible to trade Singapore or use the EFP market, the quotes were in excess of 25 ticks wide. The market was hugely illiquid. So any trader was "stuck" with what he had on the close of the session.

So now, with the aide of computer analysis, let's figure out what the sensitivities in the position actually were, with a market close of 91.00.

Position:
Fair Value $386,425
Delta 264.08
Net Delta .08
Gamma(per 50 ticks) 105.33
Vega $9180
Theta -$1615

This analysis means that the position is long premium. The cash vaue of the long options is $386k. The position is delta neutral at an underlying price of 91.00. This means that we have limited our risk top the "2nd derivatives" of gamma, vega and theta. We only need to be concerned with wolatility risk and the decay factors.

The gamma tells us that if the market moves 50 ticks, we create 105 long futures. And conversely, on a 50 tick move down, we create 105 short futures. So if the volatility is constant, in a move to 91.50, we'd have a net of 105 additional "implied" futures. And, we'd profit by 105*50*2500.
That is: $1.31 million. But, as we already stated, that is highly unlikely. The market expected move is only 6 ticks. And in a big move, it is often the case that the market moves, and then implied volatility dies.

The vega tells us that if volitility drops 1%, we lose $9180.
But if the volatility goes up 1%, we make that amount, assuming no move in the futures. And finally the theta tells us that overnight we stand to lose $1651 from premium decay.

In other words, the trader had better hope for a catastrophic market event with a position like the one above!