Programme

Rama Cont

Competition and learning in dealer markets

Price and order flow dynamics in over-the-counter (OTC) markets is driven by competition between dealers and the information extracted by dealers from market order flow. 

Game-theoretic models of market microstructure have analyzed such situations using equilibrium concepts such as Nash equilibrium, which corresponds to a benchmark situation of competitive market, but without describe the process by which the market may (or may not) reach such an equilibrium. We investigate competition and the influence of learning dynamics in this setting using mean field deep reinforcement learning. We sh§ow that, in a homogeneous population of dealers, learning may lead to  tacit collusion and supra-competitive quoting strategies, while the introduction of heterogeneity mitigates this effect.

 Patrick Cheridito

Asset pricing in an economy with changing sentiment and price feedback

We propose a continuous-time equilibrium model with a representative agent that is subject to stochastically fluctuating sentiments. Sentiments dynamically respond to past price movements and exhibit jumps, which occur with higher frequency when sentiments are more disconnected from underlying fundamentals. We model feedback effects between asset prices and sentiment in both directions. Our analysis shows that in equilibrium, sentiments affect prices even though they have no direct impact on the asset’s fundamentals. Empirically, the equilibrium risk premia and risk-free rate respond to measurable shifts in sentiment in the direction predicted by the model.

Marko Weber 

Heterogeneous Beliefs with Uninsurable Income

I study the general equilibrium of a pure-exchange economy with several agents who receive uninsurable income, trade a dividend-paying stock, and borrow from and lend to each other. Agents are heterogeneous in risk-aversion and time-preference, and hold differing beliefs on the growth rates of both the dividend and all agents' incomes. I find closed-form expressions for the interest rate, the stock price, and the agents' consumption and investment policies in equilibrium. Positive correlation of the optimists' incomes with the dividend process lowers the interest rate; in equilibrium beliefs on hedgeable processes and those on unhedgeable incomes are aggregated differently; agents with atypical beliefs have high subjective utility, but potentially unboundedly negative expected utility under the objective probability measure.

Ulrich Horst

A Mean-Field Game of Market Entry - Portfolio Liquidation with Trading Constraints

We consider both N-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initially short position of stocks are only allowed to buy while players with an initially long position are only allowed to sell the stock. Under suitable conditions on the model parameters we show that the games are equivalent to games of timing where the players need to determine the optimal times of market entry and exit. We identify the equilibrium entry and exit times and prove that equilibrium mean-trading rates can be characterized in terms of the solutions to a highly non-linear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium both in the mean-field and the N-player game. The talk is based on joint work with Guanxing Fu and Paul Hager

Julian Sester

Non-concave distributionally robust stochastic control in a discrete time finite horizon setting

In this talk we present a general framework for non-concave distributionally robust stochastic control problems in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent ambiguity sets of probability measures comprising, as a natural example, the ambiguity set defined via Wasserstein-balls around path-dependent reference measures, as well as parametric classes of probability distributions. We establish a dynamic programming principle which allows to derive both optimal control and worst-case measure by solving recursively a sequence of one-step optimization problems. As a concrete application, we study the robust hedging problem of a financial derivative under an asymmetric (and non-convex) loss function accounting for different preferences of sell- and buy side when it comes to the hedging of financial derivatives. As our entirely data-driven ambiguity set of probability measures, we consider Wasserstein-balls around the empirical measure derived from real financial data. We demonstrate that during adverse scenarios such as a financial crisis, our robust approach outperforms typical model-based hedging strategies such as the classical Delta-hedging strategy as well as the hedging strategy obtained in the non-robust setting with respect to the empirical measure and therefore overcomes the problem of model misspecification in such critical periods. (joint work with Ariel Neufeld)

Yan Dolinsky

Explicit Computations for Delayed Semistatic Hedging

In this work we consider the exponential utility maximization problem in the framework
of semistatic hedging. In addition to the usual setting considered in Mathematical Finance, we also consider an investor who is informed about the risky asset’s price changes with a delay. In the case where the stock increments are i.i.d. and normally distributed we compute explicitly the value of the problem and the corresponding optimal hedging strategy in a discrete time setting. Our approach is based on duality theory and tools from Linear Algebra which are related to banded matrices and Toeplitz matrices. Finally , we study an analogous continuous time model problem. (joint work with Or Zuk).

Samuel Cohen

Hawkes processes, delays and Limit order books

Hawkes processes are a key modelling tool for many problems, in particular for high frequency financial data. In this talk we will consider some of the difficulties which arise when working with these processes and their variations - how to account for time-dependence, non-Markovian behaviour, very large amounts of data, etc... We will present a new family of calibration methodologies which can avoid these issues and work well in practice, based on an unusual application of stochastic gradient descent. We will also apply these methods to limit order book data.

Samuel Drapeau

On/Off Shore Currency Rate Discrepancy

Most developing countries (especially in Asia) adopted a tight control of foreign capital in order to protect their economy from abrupt capital outflows in period of crisis. As those economies developed and opened up to foreign financial investment, they often set up off shore currency exchange markets to facilitate the transfer of capital. This is for instance the case of China where the on shore RMB (CNY) was complemented with an off shore market for trading this currency (CNH). Theoretically, the face value from a domestic viewpoint of the currency is the same regardless of on/off shore origin. And indeed, the CNY and the CNH spot rates only differ marginally. However, when looking at the price of futures for longer maturity, there is a significant discrepancy (in the CNY/CNY case, up to 4% when corrected for maturity). This is puzzling as the futures are written on the same underlying. In the present work we propose a mixed discrete/continuous time equilibrium in two similar markets. This solution of which is given by a coupled quadratic jump diffusion FBDEs with McKean-Vaslov component that provide an equilibrium price on both markets.
It involves stochastic transaction costs as well as stochastic supply. We then use a second equilibrium to price futures and therefore provide some interpretations as for the price discrepancy observed on the market.
This is a joint work with Xuan Tao, Peng Luo and Wang Tan.

Xiu Dacheng

Can Machines Learn Weak Signals

In high-dimensional regression scenarios with low signal-to-noise ratios, we assess the predictive performance of several prevalent machine learning algorithms. Theoretical insights show Ridge regression’s superiority in exploiting weak signals, surpassing a zero benchmark. In contrast, Lasso fails to exceed this baseline, indicating its learning limitations. Simulations reveal that Random Forest generally outperforms Gradient Boosted Regression Trees when signals are weak. Moreover, Neural Networks with l2-regularization excel in capturing nonlinear functions of weak signals. Our empirical analysis across six economic datasets suggests that the weakness of signals, not necessarily the absence of sparsity, may be Lasso’s major limitation in economic predictions.