Assessing Volatility Risk and Model Risk in Optimal Execution
35 Pages Posted: 25 Nov 2019
Date Written: November 20, 2019
We analyze the optimal liquidation problem considering stochastic volatility and model uncertainty. As a reference model, we take an extension of the classical continuous-time Almgren-Chriss model, assuming that the bid price of the traded asset has a volatility driven by a scalar Markov diffusion. In addition, we also assume that the agent is averse to model misspecification. Thus, the optimization also aims to pick the best model out of a suitable class of candidate models. We discuss the main qualitative changes in the optimal strategy obtained under these assumptions, and compare it with classical results. In order to better understand the optimal solutions, we consider two asymptotic expansions. These lead to closed-form approximations of the optimal liquidation strategy. The first expansion explores the case of an agent that is weakly ambiguous with respect to the reference model. The second one follows the Taylor series expansion method, allowing us to expand optimal solutions with respect to the state variable corresponding to the volatility driver process. We also carry out numerical experiments to illustrate the behavior of the optimal strategy, as well as the quality of the approximations obtained.
Keywords: volatility risk, model risk, liquidation, acquisition, optimal control, asymptotic expansions
JEL Classification: C61, C65, D81, G11
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