CFMAR Seminar by Moritz Voss (PSTAT VAP)

Title: Dynamic hedging in illiquid financial markets

Abstract:

We consider a variant of the limit order book model by Obizhaeva and Wang (2013) which allows for both selling and buying stock. Specifically, our price impact model determines bid- and ask-prices via a coupled system of controlled diffusions, allowing us to retain the possibility to specify market depth, tightness and resilience; the three dimensions of liquidity identified by Kyle (1985) which induce convex liquidity costs on trading strategies. We discuss the problem of utility-based hedging of contingent claims in this model. In the limit for high resilience, we argue how the hedging problem can be reduced to a considerably simpler linear quadratic optimal tracking problem of a frictionless target hedging strategy in an Almgren and Chriss (2001) type setup. We solve this problem explicitly for general predictable target strategies. It turns out that the optimal policy trades towards a weighted average of expected future target positions generalizing an insight from Gârleanu and Pedersen (2013) from their homogenous Markovian optimal investment problem to a general hedging problem. From a financial point of view, our results allow for an intuitively appealing interpretation and yield sensible hedging strategies in illiquid financial markets.

The talk is based on joint work with Peter Bank (TU Berlin) and H. Mete Soner (ETH Zurich).