Options Trading as a Game Mike Lipkin Quant

Options Trading as a Game Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 1

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

Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 3

Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 4

Dynamics: Everything on the Screen is time-varying at highfrequency. 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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 5

Four Possible Model Types for Screen Representation: A) An equilibrium (read arbitrage-free) state; no highfrequency 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 Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 6

Black-Scholes, et al. , (CEV, VG, …) belong to the first class a) b) c) Options have unique prices that change continuously with time (although stock prices may be subject to deltafunction 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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 7

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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 8

In actual floor and screen trading, all these conditions are violated. t= tnow Mike Lipkin tchar texp- Quant. Congress Europe/New. York November 2005/Stern February 2006 texp 9

Market-Maker as Maxwell’s Demon “Sell 300 May 50’s at $1. 80” Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 10

Real Options Pricing is Path-Dependent. Into the Trenches…. As an example, we concentrate on XYZ Nov 50 calls for the next several slides. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 11

XYZ Nov 50 C 1. 40 1. 60 (200 x 200) 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” Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 12

Time-line for the two scenarios: A: B: Mike Lipkin 1. 50 1. 60 1. 50 10: 03: 00 : 29 : 30 : 31 10: 04: 00 1. 50 1. 45 1. 50 Quant. Congress Europe/New. York November 2005/Stern February 2006 13

Response to SIZE trading: XYZ: 32. 60 32. 70 (400 x 750) 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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 14

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 50 C 1. 80 1. 95 (800 x 500) Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 15

LEANING: Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 16

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!! Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 17

VALUATION: During all this flurry of trading, the market-makers are adjusting 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¢. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 18

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 P 14 14. 40 Trader: Feb 40 puts, 14. 40 for 50 Specialist: 32 there. You bought them. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 19

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 (200 x 200) 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? Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 20

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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 21

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 Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 22

RISK: So supply and demand is the principle reason for marketmakers 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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 23

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) -900 K = visit to unemployment, sale of apartment, etc… Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 24

Risk Scenario, cont… ZYX Oct 80 C 0. 90 1. 05 (200 x 200) 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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 25

Risk, cont… Many factors contribute to the net safety of a trader’s position: a) b) c) d) e) Net calls Net puts Vega Dividend/interest rate Decay Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 26

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) Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 27

Takeovers (An abbreviated option board: ) Oct 30 C 6. 5 Dec 30 C 8. 5 Apr 30 C 11. 25 Oct 40 C 2. 5 Dec 40 C 3. 75 Apr 40 C 5. 85 Oct 50 C 1. 25 Dec 50 C 2. 75 Apr 50 C 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? Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 28

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? Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 29

Takeovers, cont… Specialist: . 80 -1. 25 500 -up. What would you rather do? Buy or sell the 1 x 2? 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 1 x 2. The 30 calls make $23, the 40 calls make $13. 232(13)= -3. Anyone buying the 1 x 2 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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 30

EDS after takeover rumors began 4 March, 2004 Mar 20 53 vol; Mar 22. 5 58 vol; Sep 30 32 vol. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 31

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. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 32

The Real World • Goldman Sachs paid US $7 B 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 $11 M (2004). Conclusion: Profits come from Arbitrage not Equilibrium. Mike Lipkin Quant. Congress Europe/New. York November 2005/Stern February 2006 33