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