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

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Presentation on theme: "Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 1 Options Trading as a Game."— Presentation transcript:

1 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 1 Options Trading as a Game

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

3 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 3

4 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 4

5 Mike LipkinQuantCongress 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.

6 Mike LipkinQuantCongress 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

7 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 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 be unchanged as t 0. 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 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 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 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 9 In actual floor and screen trading, all these conditions are violated. t= t now t char t exp - t exp

10 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 10 Market-Maker as Maxwells Demon Sell 300 May 50s at $1.80

11 Mike LipkinQuantCongress 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.

12 Mike LipkinQuantCongress 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

13 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 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 Mike LipkinQuantCongress 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: 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.

15 Mike LipkinQuantCongress 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)

16 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 16 LEANING:

17 Mike LipkinQuantCongress 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!!

18 Mike LipkinQuantCongress 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 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¢.

19 Mike LipkinQuantCongress 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 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 P14 14.40 Trader: Feb 40 puts, 14.40 for 50 Specialist: 32 there. You bought them.

20 Mike LipkinQuantCongress 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?

21 Mike LipkinQuantCongress 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.

22 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 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 Mike LipkinQuantCongress 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.

24 Mike LipkinQuantCongress 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…

25 Mike LipkinQuantCongress 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.

26 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 26 Risk, cont… Many factors contribute to the net safety of a traders position: a)Net calls b)Net puts c)Vega d)Dividend/interest rate e)Decay

27 Mike LipkinQuantCongress 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)

28 Mike LipkinQuantCongress Europe/NewYork November 2005/Stern February 2006 28 Takeovers (An abbreviated option board:) Oct 30C6.5Dec 30C 8.5 Apr 30C 11.25 Oct 40C2.5Dec 40C 3.75 Apr 40C 5.85 Oct 50C 1.25Dec 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?

29 Mike LipkinQuantCongress 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?

30 Mike LipkinQuantCongress 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 dont have to prove to the SEC that people know a deal is imminent. The order flow has told us.

31 Mike LipkinQuantCongress 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.

32 Mike LipkinQuantCongress 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.

33 Mike LipkinQuantCongress 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.


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