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!

EDZ87 +264

Strike***Puts***Calls
92.50****-----*** +45
92.00****----****-56
91.50****-25***+172
91.00****-05****+45
90.50****-25****+223
90.00***+102****-25
89.50****-54****+35
89.00****+75-----****


Take a look at the position.
What can we tell about the position with puts and call netted?
If the market is at 91.00 and the market moves up to 91.50,
the position at the 91.50 strike would look like that at the 91.00 strike when the market is at 91.00. And the 92.00 strike options would "look" like the 91.50 do at market price 91.00.
So the corresponding position would now look just like the following if the market moved to 91.50:


EDZ87 +264
Shifted
Strike***Net
(92.00)****+45
(91.50)****-56
(91.00)****+147
(90.50)****+35
(90.00)****+198
(89.50)****+77
(89.00)****-19
(88.50)****+75


So in a 50 tick higher move, we'd make some from a parallel shift in volatility. But, as the options at the 90 strike becomes more intrinsic (in the money) than time premium (that which is abive and beyond the strike, we get hurt on steady or lower volatility from the +147 long premium at the (not shifted) 91.50 strike.

The point is that because time premium collapses "at the money", a trader wants to "butterfly" the position such that the position is short the premium near the at the money strike price. The long +198 90.50 premium does not help the trader because the options "converge" to their intrinsic value.

And the trader can ballpark what would happen if the market moved 50 ticks the opposite way without any computer analysis. Now the shifted strike position looks like this:

EDZ87 +264
Shifted
Strike***Net
(93.00)****+45
(92.50)**** -56
(92.00)****+147
(91.50)****+35
(91.00)****+198
(90.50)****+77
(90.00)****-19
(89.50)****+75

OOPS! Again we get hurt from long premium at the market shifts down 50 ticks. Now the +198 90.50 strike is at the money. We get killed there if vol is hurt.

Traders want to sell straddles AT THE MONEY!!

Of course, if we have a RADICAL move to the upside or downside,this entire potion becomes one HUGE straddle. And as we all know, that event was highly unlikely, if not "impossible" before October 22, 1987! ;)

OK, Now I will try to do this...and not lose the entire post.

First, let's lay out the scenario. The big move in Eurodollar actually happened AFTER the market crash itself. The move started in the Asian markets, but after Paul Volcker assured the markets that “we will provide whatever liquidity is necessary”, the short term rates moved 325 basis points down on the open.

In the session before, implied volatility remained fairly steady. The locals (as always) sold premium and the paper did not really buy it up, either. Implied was up just a few %.
Yet, in the S&P pit acorss the floor, futures were down over 8,000 points. Leo Malamed made an appearance on the floor assuring that the markets would remain open, even when the NYSE was ordered to shut down trading early. Over in the currencies, the dollar was in a freefall.

So, being the conservative risk-adverse trader that I was, I got as delta neutral as possible, while buying up some gamma, just for the sake of it. After all, the stocks had moved 7 standard deviations. It did not make sense to me that this was a premium-selling event, certainly in the short run.

I have cobbled the following position together for the sake of example. I am in no way recommending a trade or even a methodology. I don't expect this event to repeat any time soon.

A market maker's job is to probvide lkiquidity to public orders as executed by brokers.
So, a trasder will accumulate an inventory of positions that often refelects the opposite side of what the institutional paper happens to be doing.

Using the following somwhat random delta neutral position, let's analyze a portfolion the night before the big market move.

Assuming: 91.00 EDZ87
Volatility, 17%, 47 days to expiration.

EDZ87 +264

Strike***Puts***Calls
92.50****-----*** +45
92.00****----****-56
91.50****-25***+172
91.00****-05****+45
90.50****-25****+223
90.00***+102****-25
89.50****-54****+35
89.00****+75-----****





Because of Put/call parity, we can strip out the corresponding boxes. This somewhat simplifies the position for the purposes of analysis. We can strip out the following box spreads;

5 91.00-90.50 boxes
25 90.00/89.50 boxes
Leaving:

EDZ87 +264

Strike***Puts***Calls
92.50****-----*** +45
92.00****----****-56
91.50****-25***+172
91.00****-05****+40
90.50****-20****+218
90.00***+077**** 0
89.50****-29****+10
89.00****+75-----****

Now, since we are delta neutral, we can talk of gamma and vega exposure by strike, meaning that we can net the puts and calls together. Gamma and vega analysis is considered to “2nd derivative analysis”. So, by netting the position, you can just multiply the position by the component rates of change. And it makes it really simple to see what further risk is implicit in the position.

EDZ87 +264

Strike***Net
92.50****+45
92.00**** -56
91.50****+147
91.00****+35
90.50****+198
90.00****+77
89.50****-19
89.00****+75

Obviously this position is heavily gamma and volatility exposed. It is readily apparent that were the futures to move one strike higher and volatility to die, the position would lose thousands. On the other hand, the market maker could make six figures on the anticipated market move.