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Options Trading as a Game


Market-Maker as Maxwell s Demon Real Options Pricing is Path-Dependent. Into the Trenches ... American Stock Exchange and Katama Trading, ... – PowerPoint PPT presentation

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Title: Options Trading as a Game

Options Trading as a Game
And Options Market-Making on an Exchange Floor
  • Reality, NOT Theory
  • Mike Lipkin, American Stock Exchange
  • 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 suppressing time-variations at these
    frequencies. This is not unreasonable, but it
    does not reflect the reality of exchange trading.

Four Possible Model Types for Screen
  • 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

Black-Scholes, et al., (CEV, VG,) belong to the
first class
  1. 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 be unchanged as
  2. Stock prices move randomly according to the
    underlying (perhaps Brownian) process, with
    usually a drift bias provided by the risk-free
  3. Markets are frictionless so transaction costs may
    be ignored.

  • 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.

  • In actual floor and screen trading, all these
    conditions are violated.

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  • Market-Maker as Maxwells Demon

Sell 300 May 50s at 1.80
Real Options Pricing is Path-Dependent. Into the
As an example, we concentrate on XYZ Nov 50
calls for the next several slides.
  • XYZ Nov 50 C 1.40 1.60 (200x200)
  • Scenario A
  • 100300 initial market
  • 100330 Buy 50 calls at the market
  • 100400 Sell 50 calls at 1.50
  • Scenario B
  • 100300 initial market
  • 100330 Sell 50 calls at 1.50
  • 100400 Buy 50 calls at the market

Time-line for the two scenarios
A 1.50 1.50 1.60 1.50 1.50
100300 29 30 31 100400
B 1.50 1.50 1.45 1.45
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 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.

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)

  • 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.
  • A LOT, maybe 125,000!!

  • During all this flurry of trading, the
    market-makers are adjusting 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 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.

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 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.

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
  • 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?

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.

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

  • 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.

  • Consider a trader with the following risk
  • Stock ZYX at 65.75
  • Up 25 he loses 900,000
  • Down 25 he makes 80,000
  • (volatilities unchanged for this simple
  • -900K visit to unemployment, sale of apartment,

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.

Risk, cont
  • Many factors contribute to the net safety of a
    traders position
  • Net calls
  • Net puts
  • Vega
  • Dividend/interest rate
  • 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
  • b) too long premium (decay risk for small
    movements and contraction risk for steady up
  • c) volatility risk (especially long term
  • d) interest rates
  • e) take-over risk
  • f) hard-to-borrow (buy-in risk)

  • (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
  • Broker Give me a market in the Oct 30-40 1-by-2.
  • The screen value is 1.50. What market does he

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. 23-2(13) -3. Anyone buying the 1x2 loses 3
    on the spread PLUS what he paid for it.
  • We dont have to prove to the SEC that people
    know a deal is imminent. The order flow has told

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
  • Hysteresis is real in option prices. Implied
    volatilities depend greatly on the recent stock
  • 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.

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
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