We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps clustering features. Models of this kind have been already proposed for the spot price dynamics, but the main purpose of the present work is to investigate the performances of such models in describing the forward dynamics. We adopt a Heath-Jarrow-Morton approach in order to capture the whole forward curve evolution. By examining daily data in the French power market, we perform a goodness-of-fit test and we present our conclusions about the adequacy of these models in describing the forward prices evolution.

In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for a large number of bonds to asset managers from all around the globe. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. Useful models exist, most of them inspired by that of Avellaneda and Stoikov. These models describe the complex optimization problem faced by market makers: proposing bid and ask prices in an optimal way for making money out of the difference between bid and ask prices while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving numerically the equations characterizing the optimal bid and ask quotes is seldom tackled in the literature, especially in high dimension. In this paper, our goal is to propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model \`a la Avellaneda-Stoikov. Because we aim at considering a large universe of bonds, classical finite difference methods as those discussed in the literature cannot be used and we present therefore a discrete-time method inspired by reinforcement learning techniques. More precisely, the approach we propose is a model-based actor-critic-like algorithm involving deep neural networks.

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

We discuss a simple, exactly solvable model of stochastic stock dynamics that incorporates regime switching between healthy and distressed regimes. Using this model, which is analytically tractable, we discuss a way of extracting expected returns for stocks from realized CDS spreads, essentially, the CDS market sentiment about future stock returns. This alpha/signal could be useful in a cross-sectional (statistical arbitrage) context for equities trading.

Cultural trends and popularity cycles can be observed all around us, yet our theories of social influence and identity expression do not explain what perpetuates these complex, often unpredictable social dynamics. We propose a theory of social identity expression based on the opposing, but not mutually exclusive, motives to conform and to be unique among one's neighbors in a social network. We then model the social dynamics that arise from these motives. We find that the dynamics typically enter random walks or stochastic limit cycles rather than converging to a static equilibrium. We also prove that without social network structure or, alternatively, without the uniqueness motive, reasonable adaptive dynamics would necessarily converge to equilibrium. Thus, we show that nuanced psychological assumptions (recognizing preferences for uniqueness along with conformity) and realistic social network structure are both necessary for explaining how complex, unpredictable cultural trends emerge.

We develop a new market-making model, from the ground up, which is tailored towards high-frequency trading under a limit order book (LOB), based on the well-known classification of order types in market microstructure. Our flexible framework allows arbitrary order volume, price jump, and bid-ask spread distributions as well as the use of market orders. It also honors the consistency of price movements upon arrivals of different order types. For example, it is apparent that prices should never go down on buy market orders. In addition, it respects the price-time priority of LOB. In contrast to the approach of regular control on diffusion as in the classical Avellaneda and Stoikov [1] market-making framework, we exploit the techniques of optimal switching and impulse control on marked point processes, which have proven to be very effective in modeling the order-book features. The Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI) associated with the control problem can be solved numerically via finite-difference method. We illustrate our optimal trading strategy with a full numerical analysis, calibrated to the order-book statistics of a popular Exchanged-Traded Fund (ETF). Our simulation shows that the profit of market-making can be severely overstated under LOBs with inconsistent price movements.

We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By weak feedback we mean the case where the contagion parameters are small enough to prevent blow-ups in solutions. Next, we specialise to a Brownian driver and show how the same techniques can be extended to give short-time uniqueness after blow-ups, regardless of the feedback strength. The heart of our approach is a surprisingly simple probabilistic comparison argument that is robust in the sense that it does not ask for any regularity of the solutions.

This paper focuses on the weekly idiosyncratic momentum (IMOM) as well as its risk-adjusted versions with respect to various idiosyncratic risk metrics. Using the A-share individual stocks in the Chinese market from January 1997 to December 2017, we first evaluate the performance of the weekly momentum and idiosyncratic momentum based on raw returns and idiosyncratic returns, respectively. After that the univariate portfolio analysis is conducted to investigate the return predictability with respect to various idiosyncratic risk metrics. Further, we perform a comparative study on the performance of the IMOMportfolios with respect to various risk metrics. At last, we explore the possible explanations to the IMOM as well as risk-based IMOM portfolios. We find that 1) there is a prevailing contrarian effect and a IMOM effect for the whole sample; 2) a negative relation exists between most of the idiosyncratic risk metrics and the cross-sectional returns, and better performance is found that is linked to idiosyncratic volatility (IVol) and maximum drawdowns (IMDs); 3) additionally, the IVol-based and IMD-based IMOM portfolios exhibit a better explanatory power to the IMOM portfolios with respect to other risk metrics; 4) finally, higher profitability of the IMOM as well as IVol-based and IMD-based IMOM portfolios is found to be related to upside market states, high levels of liquidity and high levels of investor sentiment.