Options Trading as a Game
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
1
And
Options Market-Making on an
Exchange Floor
Reality, NOT Theory
Mike Lipkin,
Mike Lipkin
American Stock Exchange and
Katama Trading, LLC
QuantCongress Europe/NewYork
November 2005/Stern February 2006
2
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
3
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
4
Dynamics: Everything on the Screen is time-varying at highfrequency.
Nevertheless: Economists (especially), Financial
Mathematicians, Physicists, etc. have attempted to model
what prices are seen on the screen, often by suppressing
time-variations at these frequencies. This is not
unreasonable, but it does not reflect the reality of exchange
trading.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
5
Four Possible Model Types for Screen
Representation:
A) An equilibrium (read arbitrage-free) state; no highfrequency 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
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
6
Black-Scholes, et al., (CEV, VG,…) belong to the
first class
a)
b)
c)
Options have unique prices that change continuously
with time (although stock prices may be subject to deltafunction impulses: Brownian motion or even jumps). If
the stock price is unchanged, the option price will be
unchanged as t0.
Stock prices move randomly according to the underlying
(perhaps Brownian) process, with usually a drift bias
provided by the risk-free rate.
Markets are frictionless so transaction costs may be
ignored.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
7
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 independent of other factors
especially (but not limited to) supply and demand for
options and stock.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
8
In actual floor and screen trading, all these
conditions are violated.
t= tnow
Mike Lipkin
tchar
texp-
QuantCongress Europe/NewYork
November 2005/Stern February 2006
texp
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Market-Maker as Maxwell’s Demon
“Sell 300 May 50’s at $1.80”
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
10
Real Options Pricing is Path-Dependent. Into
the Trenches….
As an example, we concentrate on XYZ Nov
50 calls for the next several slides.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
11
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 $1.50”
10:04:00 “Buy 50 calls at the market”
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
12
Time-line for the two scenarios:
A:
B:
Mike Lipkin
1.50
1.50 1.60 1.50
1.50
10:03:00
:29 :30 :31
10:04:00
1.50
1.50 1.45 1.45
1.50
QuantCongress Europe/NewYork
November 2005/Stern February 2006
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Response to SIZE trading:
XYZ: 32.60 32.70 (400x750)
Broker: Nov 50 calls, size market.
Specialist: 1.40-1.60, 500-up; 1.30-1.70, 1000-up
Broker: I’ll 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, I’ll try to clear the away market….I only bought
100 at 1.70 away; there’s 500 more at 1.75, I’ll try to get
those.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
14
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)
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
15
LEANING:
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
16
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!!
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
17
VALUATION:
During all this flurry of trading, the market-makers are
adjusting the theoretical valuations of the options. WHY?
Because traders don’t input the measured stock volatility of a
model and get a price. They plug the trading price of the
option 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 the
price has increased by 30¢.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
18
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 45’s and 50’s by 3 points.
This is all heuristic, seat-of-the-pants fiddling. When he does
this, 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 50
Specialist: 32 there. You bought them.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
19
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, selling puts, buying calls and stock.
Specialist: 2.65-2.85 200-up
Broker: Where do 500 come?
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
20
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.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
21
Real World Example:
•
•
On September 16, 2005, a BA customer sold 150,000
FDC Jan 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
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
22
RISK:
So supply and demand is the principle reason for marketmakers 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.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
23
Scenario
Consider a trader with the following risk profile:
Stock ZYX at 65.75
Up 25% he loses $900,000
Down 25% he makes $80,000
(volatilities unchanged for this simple example)
-900K = visit to unemployment, sale of apartment, etc…
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
24
Risk Scenario, cont…
ZYX Oct 80 C
0.90 1.05 (200x200)
Naïve valuation is $0.98.
Trader: ZYX Oct 80 calls, 1 bid for 500.
Others in Crowd: sell 30, sell 25….
Trader: I bought 90, 1.05 bid for the balance.
In practice, the trader may be buying on several markets
electronically.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
25
Risk, cont…
Many factors contribute to the net safety of a trader’s
position:
a)
b)
c)
d)
e)
Net calls
Net puts
Vega
Dividend/interest rate
Decay
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
26
Risk, cont…
These concerns can be rewritten in more suggestive terms.
Some risk factors are:
a) too short premium (blow out risk for big moves)
b) too long premium (decay risk for small movements and
contraction risk for steady up moves)
c) volatility risk (especially long term contracts)
d) interest rates
e) take-over risk
f) hard-to-borrow (buy-in risk)
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
27
Takeovers
(An abbreviated option board:)
Oct 30C
6.5
Dec 30C 8.5 Apr 30C 11.25
Oct 40C
2.5
Dec 40C 3.75 Apr 40C 5.85
Oct 50C 1.25
Dec 50C 2.75 Apr 50C 4.80
XYZ is trading 30 at the end of September. The 50 strike is
the highest strike available.
All of a sudden, the order flow in the Apr 50 calls becomes
brisk and one-way.
Can you guess which way?
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
28
Takeovers, cont…
Brokers (or electronically): Sell 200; Sell 300; Sell 500…
No one consults a theory. The implied volatility on all the 50
lines gets crushed; the volatility in the late months gets
reduced.
At the same time orders come in for strange spreads:
Broker: Give me a market in the Oct 30-40 1-by-2.
The screen value is $1.50. What market does he get?
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
29
Takeovers, cont…
Specialist: .80-1.25 500-up.
What would you rather do? Buy or sell the 1x2?
What if XYZ is acquired for $53 in cash? The premium on
the options will all fall to near $0! The Apr 50 calls will be
worth $3, less than they are now!
The 1x2. The 30 calls make $23, the 40 calls make $13. 232(13)= -3. Anyone buying the 1x2 loses $3 on the spread
PLUS what he paid for it.
We don’t have to prove to the SEC that people know a deal is
imminent. The order flow has told us.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
30
EDS after takeover rumors began 4 March, 2004
Mar 20 53 vol; Mar 22.5 58 vol; Sep 30 32 vol.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
31
Conclusion and Summary
• Option prices on the floor are determined by supply and
demand first, theory second.
• The perception and reality of risk changes the values paid
for options independent of order flow.
• Hysteresis is real in option prices. Implied volatilities
depend greatly on the recent stock path.
• Game theory and/or the physics of driven dynamical
systems may provide a better approach to market analysis.
• Possible BIG IDEA: takeovers instead of defaults.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
32
The Real World
• Goldman Sachs paid US $7B for Spear Leads and
Kellogg (2001).
• SLK option market-making accounted for ca. 15%
of their profits (nearly half on AMEX).
• GS tried to automate (read: apply
thermodynamics) to options specialist book.
• GS sells AMEX book back to original SLK
partners for US $11M (2004).
Conclusion: Profits come from Arbitrage not
Equilibrium.
Mike Lipkin
QuantCongress Europe/NewYork
November 2005/Stern February 2006
33