Lipkin Options

7/28/2019 Lipkin Options

http://slidepdf.com/reader/full/lipkin-options 1/33

Mike Lipkin QuantCongress Europe/NewYork November 2005/Stern February 2006

1

Options Trading as a Game




2

AndOptions Market-Making on an

Exchange Floor

Reality, NOT Theory

Mike Lipkin, American Stock Exchange and

Katama Trading, LLC




3




4




5

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.




6

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




7

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.




8

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.




9

In actual floor and screen trading, all these

conditions are violated.

t= tnow tchar texp- texp




10

Market-Maker as Maxwell’s Demon

“Sell 300 May 50’s at $1.80”




11

Real Options Pricing is Path-Dependent. Into

the Trenches….

As an example, we concentrate on XYZ Nov

50 calls for the next several slides.




12

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”




13

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




14

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-upBroker: 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.




15

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)




16

LEANING:




17

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!!




18

VALUATION:

During all this flurry of trading, the market-makers areadjusting 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 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 the price has increased by 30¢.




19

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 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.




20

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?




21

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.




22

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




23

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.




24

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…




25

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 26

Risk, cont…

Many factors contribute to the net safety of a trader’s

position:

a) Net calls

b) Net puts

c) Vega

d) Dividend/interest ratee) Decay




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 andcontraction risk for steady up moves)

c) volatility risk (especially long term contracts)

d) interest ratese) take-over risk

f) hard-to-borrow (buy-in risk)




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?




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?




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 beworth $3, less than they are now!

The 1x2. The 30 calls make $23, the 40 calls make $13. 23-

2(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.




EDS after takeover rumors began 4 March, 2004

Mar 20 53 vol; Mar 22.5 58 vol; Sep 30 32 vol.




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/NewYorkN b 2005/St F b 2006 33

The Real World

• Goldman Sachs paid US $7B for Spear Leads andKellogg (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.

Lipkin Options

Documents

Transcript of Lipkin Options