Finance and Economics

• Liquidity and Information in Order Driven Markets
  (Abstract, April 2008)
  
  • This paper analyzes the interaction between liquidity traders and informed traders and their choice between market and limit orders. If the patient informed people see a fundamental value far from the efficient price, they optimally become impatient and submit market orders instead of limit orders.
• A Dynamic Model of the Limit Order Book
  (June 2008,   Revise and Resubmit, RFS)
  
  • In this model, buy and sell prices arise from the interaction of patient and impatient liquidity traders who arrive randomly to the market and have a choice between market and limit orders. An equilibrium limit order book is derived.
• Is Liquidity Caused by Trading Activity? Weather and Trading in a Limit Order Market,   with Juhani Linnainmaa
  (Abstract, February 2008)
  
  • We show that trading activity and trading competition cause liquidity in Finland's fully electronic market. We use weather and lagged US returns as instruments.
• Multi-Stage Game Theory in Continous Time
  (January 2006)
  
  • I define multi-stage game theory in continuous time, including mixed strategies. Mixing can be done both over time and over actions. I also define "layered times" which allow for stopping the clock.
• A CAPM with Price Impact,   with Andrew Lo and Jiang Wang
  (Abstract, December 2005)
  
  • This model shows that if a large investor trades to hedge private (e.g. labor income) shocks, then stock returns should display a liquidity premium. The premium increases with the price impact coefficient, and with the correlation to stocks with lower price impact.
• The Success Probability and Synergies of a Tender Offer via Stock and Option Prices,   with Victor Martinez
  (November 2005)
  
  • When a takeover is announced but has not yet completed, there are several implicit sources of uncertainty: the probability of success, the synergies of the merger, and the fall-back prices (prices if the deal fails). We propose a model to consistently price options on the companies involved in the merger. Then we use this model to estimate the various sources of uncertainty using a method borrowed from Bayesian statistics (Markov-Chain Monte Carlo).
• On the Derivation of the Black-Scholes formula,   with Dan Stroock
  (Published in Séminaire de Probabilités 37 (2004), 399-414)
  
  • This paper gives a rigorous proof of the Black-Scholes formula using the original bond replication method. Unlike the (Merton) call replication method, the original argument has never been made rigorous until now, as far as I know.
• Limit Order Markets, Liquidity, and Price Impact
  (PhD thesis - Abstract, June 2004)