Lipkin Options

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Mike Lipkin QuantCongress Europe/NewYorkNovember 2005/Stern February 2006
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Options Trading as a Game

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AndOptions Market-Making on an
Exchange Floor
Reality, NOT Theory
Mike Lipkin, American Stock Exchange and
Katama Trading, LLC

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Dynamics: Everything on the Screen is time-varying at high-
frequency.
Nevertheless: Economists (especially), Financial
Mathematicians, Physicists, etc. have attempted to model
what prices are seen on the screen, often by suppressingtime-variations at these frequencies. This is not
unreasonable, but it does not reflect the reality of exchange
trading.

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Four Possible Model Types for Screen
Representation:
A) An equilibrium (read arbitrage-free) state; no high-
frequency dynamics (thermodynamics)
B*) A far-from-equilibrium state
C*) A dynamical steady-state
D) A game board between moves
*-dynamics to be supplied -rules for moves to be supplied

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Black-Scholes, et al., (CEV, VG,) belong to the
first class
a) Options have unique prices that change continuously
with time (although stock prices may be subject to delta-
function impulses: Brownian motion or even jumps). If
the stock price is unchanged, the option price will beunchanged as t0.
b) Stock prices move randomly according to the underlying
(perhaps Brownian) process, with usually a drift bias
provided by the risk-free rate.
c) Markets are frictionless so transaction costs may be
ignored.

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d) A consistent valuation of option prices needs the
underlying variables of the stock process: interest rates,
volatility or standard deviation of the stock price
movement, dividend dates and amounts, etc.
BUT:
e) Option valuation is independentof other factors
especially (but not limited to) supply and demand for
options and stock.

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In actual floor and screen trading, all these
conditions are violated.
t= tnow tchartexp- texp

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Market-Maker as Maxwells Demon
Sell 300 May 50s at $1.80

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Real Options Pricing is Path-Dependent. Into
the Trenches.
As an example, we concentrate on XYZ Nov
50 calls for the next several slides.

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XYZ Nov 50 C 1.40 1.60 (200x200)
Scenario A:
10:03:00 initial market
10:03:30 Buy 50 calls at the market
10:04:00 Sell 50 calls at $1.50
Scenario B:
10:03:00 initial market
10:03:30 Sell 50 calls at $1.5010:04:00 Buy 50 calls at the market

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Time-line for the two scenarios:
10:03:00 :29 :30 :31 10:04:00
A: 1.50 1.50 1.60 1.50 1.50
B: 1.50 1.50 1.45 1.45 1.50

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Response to SIZEtrading:
XYZ: 32.60 32.70 (400x750)
Broker: Nov 50 calls, size market.
Specialist: 1.40-1.60, 500-up; 1.30-1.70, 1000-upBroker: Ill pay up to $1.80 for 5000!
---
Specialist: You bought 500 at 1.60, 500 more at 1.70; the ISE
is at 1.70, Ill try to clear the away market.I only bought
100 at 1.70 away; theres 500 more at 1.75, Ill try to get
those.

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Size trading continued
Suppose that a lot of stock is available at $32.70 (unlikely!!)
Specialist: How many have you done so far (through $1.75)?
Broker: 3500, $1.80 bid for 1500.
Some traders have an oversupply of premium.
Traders: Sell 100; Sell 50; Sell 100; etc.
When all are done (and the away markets are cleared) the
broker still is bidding for 800. The new market reads:
Nov 50C 1.80 1.95 (800x500)

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LEANING:

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An estimate of the deltas for the XYZ Nov 50 calls with the
stock at $32.70 might be 20.
The broker has bid for 100,000 deltas. So far he has bought
84,000.
HOW MUCH STOCK HAS THE CROWD BOUGHT?
A LOT, maybe 125,000!!

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VALUATION:
During all this flurry of trading, the market-makers areadjusting the theoretical valuations of the options. WHY?
Because traders dont input the measured stock volatility of a
model and get a price. They plug the trading price of theoption into a model and arrive at a volatility.
When trading began, Nov 50 calls were worth $1.50; now
they are valued at $1.80+. So without the stock moving theprice has increased by 30.

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Valuation continued
A trader in the crowd has increased the volatility he uses for
Nov 50 options by 10 clicks. He raises the Dec options on
the 50 line by 5 points and the 45s and 50s by 3 points.
This is all heuristic, seat-of-the-pants fiddling. When he doesthis, it turns out that the Feb 45 puts have a new theoretical
value. Originally he thought the puts were worth $14.34.
Feb 40 P 14 14.40
Trader: Feb 40 puts, 14.40 for 50Specialist: 32 there. You bought them.

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Valuation continued
Later in the day the stock is trading 35.25. With nothing on
the book the market reads:
Nov 50 C 2.65 2.85 (200x200)
Trader A is short 500 deltas.
The same broker enters the crowd and asks for the market.
Without hearing what order the broker has, he immediately
tries to buy deltas,sellingputs, buyingcalls and stock.Specialist: 2.65-2.85 200-up
Broker: Where do 500 come?

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Valuation, cont
What is the role of an equilibrium model?
Once the new prices are stable, calendars and verticals are
priced off the standard models.

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Real World Example:
On September 16, 2005, a BA customer sold 150,000
FDCJan 40 calls to market-makers, mostly within a
two-hour window.
The implied volatility went from 23 to 19 in January and
from 28 to 20 in November.*
* at-the-money options

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RISK:
So supply and demand is the principle reason for market-
makers to change their valuations. But there is another
powerful effect, which is a direct consequence of
Options Trading as Games Playing.
That is RISK.
Strong effect on tail valuation.

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Scenario
Consider a trader with the following risk profile:
Stock ZYX at 65.75
Up 25% he loses $900,000Down 25% he makes $80,000
(volatilities unchanged for this simple example)
-900K = visit to unemployment, sale of apartment, etc

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Risk Scenario, cont
ZYX Oct 80 C 0.90 1.05 (200x200)
Nave valuation is $0.98.Trader: ZYX Oct 80 calls, 1 bid for 500.
Others in Crowd: sell 30, sell 25.
Trader: I bought 90, 1.0

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