Peng Luo | Department of Statistics and Actuarial Science, University of Waterloo
An FBSDE approach to market impact games with stochastic parameters
Market impact refers to the fact that the execution of a large order influences the price of the underlying asset. The phenomenon of price impact becomes relevant for orders that are large in comparison to the instantaneously available liquidity in markets. Market impact games analyze situations in which several agents compete for liquidity in a market impact model or try to exploit the price impact generated by competitors. In this talk I will analyze a market impact game between several risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. The first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). The second main result provides conditions under which this system of FBSDEs has indeed a unique solution, which in turn yields the unique Nash equilibrium. Closed-form solutions are obtained in special situations and numerical results are provided.