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The Execution Game: Insights in Financial Engineering with Game Theory

Delve into The Execution Game research study conducted by Beomsoo Park and team at Stanford University's Electrical Engineering Information Systems Laboratory. Explore strategic trading models, arbitrage strategies, and signaling responses to market activity. Gain valuable insights on trading policies, Perfect Bayesian Equilibrium, and more.

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The Execution Game: Insights in Financial Engineering with Game Theory

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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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