Title: Modelling Limit Order Book Data by State-Dependent Hawkes Processes PDF
Speaker: Dr Mikko Pakkanen CV
Abstract: In this talk I will present a novel variant of the Hawkes process that incorporates a state process that is fully coupled to a point process that follows Hawkes-like dynamics. The model is motivated by an application to limit order book (LOB) data, where we observe that arriving orders tend to be influenced by the state of the LOB, which then, reciprocally, changes according to the orders. After laying out the framework, I will present empirical results that illustrate the strong state dependence, in this case using the queue imbalance as state variable, of self and cross excitation in tick-by-tick LOB data. The talk is based on joint work with Maxime Morariu-Patrichi.
Title: A multi-asset investment and consumption problem with transaction costs PDF
Speaker: Dr Alex Tse CV
Abstract: We consider a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We
specialise to a case where transaction costs are zero except for sales and purchases of a single asset which we call the illiquid asset. We show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential equation. Important properties of the multi-asset problem (including when the problem is well-posed, ill-posed, or well-posed for some values of transaction costs only) can be inferred from the behaviours of a quadratic function of a single variable and another algebraic function.
Title: Uniqueness, Existence and regularity of solutions to stochastic Volterra integral equations PDF
Speaker: Dr Alexander Kalinin
Abstract: In this talk we introduce and study stochastic path-dependent Volterra integral equations in separable Hilbert spaces. Our aim is to derive unique non-extendible solutions, provide growth and error estimates for Picard iterations and establish regularity of solutions with respect to the initial data. To this end, we develop an approach to deal with path-dependent coefficients that are of Volterra type, by first considering the eterministic case when no stochastic integrals are involved.
Title: Liquidity and Asset Prices PDF
Speaker: Prof Johannes Muhle-Karbe CV
Abstract:In the first part of the talk, we study risk-sharing equilibria where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic differential equations. We show that a unique solution generally exists provided that the agents’ preferences are sufficiently similar. In a benchmark specification, the illiquidity discounts and liquidity premia observed empirically correspond to a positive relationship between transaction costs and volatility.In the second part of the talk, we discuss how the model can be calibrated to time series of prices and the corresponding trading volume, and explain how extensions of the model with general transaction costs, for example, can be solved numerically using the deep learning approach of Han, Jentzen, and E (2018). Title: Inventory Management for High-Frequency Trading with Imperfect Competition
Speaker: Prof Chen Yang
Abstract: We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs’ optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions obtain around the high-frequency limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs’ risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to a social-planner solution for cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.
Title: On the Equilibrium Strategies for Time-Inconsistent Problems in Continuous Time PDF
Speaker: Prof He Xuedong CV
Abstract: In a continuous-time setting, the existing notion of equilibrium strategies for time-inconsistent problems in the literature, referred to as weak equilibria, is not fully aligned with the standard definition of equilibria in the game theory in that the agent may be willing to deviate from a given weak equilibrium strategy. To address this issue, we propose two new notions of equilibrium strategies for time-inconsistent problems, named regular equilibria and strong equilibria. For a large class of time-inconsistent problems, we derive sufficient conditions as well as necessary conditions for a strategy to be a regular equilibrium and to be a strong equilibrium. We examine three time-inconsistent portfolio selection problems in the literature and show that the weak equilibrium strategies derived therein are also regular equilibria but are not strong equilibria. We further provide an example to show that a weak equilibrium strategy may not be a regular equilibrium. Our results suggest that the notion of regular equilibria is preferred in the study of time-inconsistent problems.This is a joint work with Zhaoli Jiang.
Title:Scoring limit orders
Speaker: Prof Gao Xuefeng CV
Abstract: In this paper, we analyse an ex ante performance measure named Order Score for limit orders at best quotes for large-tick assets. We develop a stochastic model for computing Order Score that takes into account of both the queue position of a limit order and the bid-ask queue imbalance. We calibrate our model using NASDAQ data and validate the model using backtesting simulations. We also apply our model together with bandit algorithms to guide order cancellation decisions in algorithmic trading.
Title: Deep learning and Path-dependent PDEs for rough volatility
Speaker: Dr Antoine Jacquier CV
Abstract: Volatility is rough. So do the data suggest. Since this epiphany, rough volatility models have sprouted everywhere among academics and practitioners. Their main feature is the roughness of the paths of the volatility process, well captured by a fractional Brownian motion with small Hurst exponent. This, however, breaks the beloved Markovian structure of the model, thereby restricting numerical methods to Monte Carlo simulations. We show here that a path-dependent Feynman-Kac version applies, and that the pricing problem is a solution to a path-dependent PDE (PPDE). We focus in particular on developing a numerical scheme, borrowed from the deep learning hype, that allows us to price any option.
Title: Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint PDF
Speaker: Eyal Neuman CV
Title: Systemic risk quantification via shock amplification in financial network PDF
Speaker: Prof Ahn Dohyun CV
Abstract: We consider the Eisenberg-Noe model for financial networks, focusing on random shocks to financial institutions. Using duality, we characterize shock amplification caused by the network structure and find the condition when a specific group of banks (e.g., SIFI) fails. This finding enables us to improve our understanding of shock propagation in financial networks. To be specific, we obtain robust bounds of default probabilities when only partial network information is available, and we observe that the link structure of the network contains crucial information. This is also confirmed by looking at asymptotic default probabilities in a small shock regime. With such analytical tools, systemic risk capital which prevents the default of target banks is discussed using chance-constrained optimization. All the claims are numerically illustrated by an actual European banking network.