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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 and Katama Trading, LLC. Dynamics : Everything on the Screen is time-varying at high-frequency .

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Options Trading as a Game

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  1. Options Trading as a Game QuantCongress Europe/NewYork November 2005/Stern February 2006

  2. AndOptions Market-Making on an Exchange Floor Reality, NOT Theory Mike Lipkin, American Stock Exchange and Katama Trading, LLC QuantCongress Europe/NewYork November 2005/Stern February 2006

  3. QuantCongress Europe/NewYork November 2005/Stern February 2006

  4. QuantCongress Europe/NewYork November 2005/Stern February 2006

  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 suppressing time-variations at these frequencies. This is not unreasonable, but it does not reflect the reality of exchange trading. QuantCongress Europe/NewYork November 2005/Stern February 2006

  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 QuantCongress Europe/NewYork November 2005/Stern February 2006

  7. Black-Scholes, et al., (CEV, VG,…) belong to the first class • 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. • 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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  8. 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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  9. In actual floor and screen trading, all these conditions are violated. t= tnow tchar texp- texp QuantCongress Europe/NewYork November 2005/Stern February 2006

  10. Market-Maker as Maxwell’s Demon “Sell 300 May 50’s at $1.80” QuantCongress Europe/NewYork November 2005/Stern February 2006

  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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  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” QuantCongress Europe/NewYork November 2005/Stern February 2006

  13. Time-line for the two scenarios: A: 1.50 1.50 1.60 1.50 1.50 10:03:00 :29 :30 :31 10:04:00 B: 1.50 1.50 1.45 1.45 1.50 QuantCongress Europe/NewYork November 2005/Stern February 2006

  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-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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  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) QuantCongress Europe/NewYork November 2005/Stern February 2006

  16. LEANING: QuantCongress Europe/NewYork November 2005/Stern February 2006

  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!! QuantCongress Europe/NewYork November 2005/Stern February 2006

  18. 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¢. QuantCongress Europe/NewYork November 2005/Stern February 2006

  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 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 P14 14.40 Trader: Feb 40 puts, 14.40 for 50 Specialist: 32 there. You bought them. QuantCongress Europe/NewYork November 2005/Stern February 2006

  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? QuantCongress Europe/NewYork November 2005/Stern February 2006

  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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  22. 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 QuantCongress Europe/NewYork November 2005/Stern February 2006

  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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  24. 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… QuantCongress Europe/NewYork November 2005/Stern February 2006

  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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  26. Risk, cont… Many factors contribute to the net safety of a trader’s position: • Net calls • Net puts • Vega • Dividend/interest rate • Decay QuantCongress Europe/NewYork November 2005/Stern February 2006

  27. 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) QuantCongress Europe/NewYork November 2005/Stern February 2006

  28. 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? QuantCongress Europe/NewYork November 2005/Stern February 2006

  29. 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? QuantCongress Europe/NewYork November 2005/Stern February 2006

  30. 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 don’t have to prove to the SEC that people know a deal is imminent. The order flow has told us. QuantCongress Europe/NewYork November 2005/Stern February 2006

  31. EDS after takeover rumors began 4 March, 2004 Mar 20 53 vol; Mar 22.5 58 vol; Sep 30 32 vol. QuantCongress Europe/NewYork November 2005/Stern February 2006

  32. 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. QuantCongress Europe/NewYork November 2005/Stern February 2006

  33. 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. QuantCongress Europe/NewYork November 2005/Stern February 2006

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