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The Execution Game

The Execution Game. Beomsoo Park Information Systems Laboratory Electrical Engineering Stanford University Joint work with Ciamac Moallemi and Benjamin Van Roy. Example: Société Générale. Discovery of €50B position Liquidated over January 21-23 Received €45.1B Market impact

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The Execution Game

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  1. The Execution Game Beomsoo Park Information Systems Laboratory Electrical Engineering Stanford University Joint work with Ciamac Moallemi and Benjamin Van Roy.

  2. Example: Société Générale • Discovery of €50B position • Liquidated over January 21-23 • Received €45.1B • Market impact • Triggered emergency rate cut of January 22 “cracked under the pressure of a 30 hour work week”

  3. Basic Trading Model(Bertsimas and Lo, 1998) • Initial position • Trades • Requirement • Nominal price evolution • Impact of our trades • Minimize execution cost zero-mean noise amount purchased

  4. Arbitrageur Model • Initial position • Trades • Constraint • Initial estimate • Price Dynamics • Minimize execution cost

  5. Information States • Arbitrageur • my position • estimate of his • decision policy • Trader • my position • his position • his estimate of mine • decision policy

  6. Perfect Bayesian Equilibrium (PBE) • (*,*) such that • * is the trader’s best response to (*,*) • * is the arbitrageur’s best response to * • Trading Policy Equipartitioning policy PBE policy

  7. Solving for PBE • “Shoot first, ask questions later” • Dynamic programming • Recursive computation of value functions • Trader’s value function depends on • trader’s position • arbitrageur’s position • arbitrageur’s beliefs • Arbitrageur’s value function depends on • arbitrageur’s position • arbitrageur’s beliefs probability distribution

  8. No Arbitrageur arbitrageur does nothing Average P&L trader equipartitions relative volume (0)

  9. Arbitrageur vs. Nonstrategic Trader strategic arbitrageur Average P&L trader equipartitions relative volume (0)

  10. Performance strategic arbitrageur Average P&L strategic trader relative volume (0)

  11. Signaling

  12. Response to Market Activity • Neutral market • Trader sells gradually • Accelerates at end of horizon • Down market • Regardless of trader, arbitrageur perceives selling • Arbitrageur front runs by selling • Trader sells more evenly over time • Up market • Arbitrageur perceives buying • Arbitrageur tries to front run by buying • Trader buys to front run arbitrageur • Trader profits from arbitrageur’s misunderstanding

  13. Closing Remarks • Accounting for arbitrageur activity can be important • Extensions • Multiple arbitrageurs • Uncertain trader • Infinite horizon / risk aversion • Microstructure • Role of game theory in financial engineering

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