Assessing Volatility Risk and Model Risk in Optimal Execution

35 Pages Posted: 25 Nov 2019

See all articles by Max O. Souza

Max O. Souza

Universidade Federal Fluminense - Instituto de Matemática e Estatística

Yuri Thamsten

Universidade Federal Fluminense - Instituto de Matemática e Estatística

Date Written: November 20, 2019

Abstract

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

Suggested Citation

Souza, Max and Thamsten, Yuri, Assessing Volatility Risk and Model Risk in Optimal Execution (November 20, 2019). Available at SSRN: https://ssrn.com/abstract=3492800 or http://dx.doi.org/10.2139/ssrn.3492800

Max Souza (Contact Author)

Universidade Federal Fluminense - Instituto de Matemática e Estatística ( email )

Rua Prof. Marcos Waldemar de Freitas Reis, S/N
Blocos G e H, Campus do Gragoatá,
Niterói, Rio de Janeiro 24210-201
Brazil

HOME PAGE: http://www.professores.uff.br/msouza

Yuri Thamsten

Universidade Federal Fluminense - Instituto de Matemática e Estatística ( email )

Rua Prof. Marcos Waldemar de Freitas Reis, S/N
Blocos G e H, Campus do Gragoatá,
Niterói, Rio de Janeiro 24210-201
Brazil

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