Options Trading as a Game

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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 suppressing time-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

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
   ?t?0.
2. Stock prices move randomly according to the
   underlying (perhaps Brownian) process, with
   usually a drift bias provided by the risk-free
   rate.
3. Markets are frictionless so transaction costs may
   be ignored.

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• 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.

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• 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
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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
• 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

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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
1.50
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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 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 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.

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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 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.

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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, selling puts,
  buying calls 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
  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

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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 900,000
• Down 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)
• 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.

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Risk, cont

• Many factors contribute to the net safety of a
  traders position
• Net calls
• Net puts
• Vega
• Dividend/interest rate
• Decay

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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)

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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?

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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?

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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
  us.

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EDS after takeover rumors began 4 March, 2004
Mar 20 53 vol Mar 22.5 58 vol Sep 30 32 vol.
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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.

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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.