Quantitative Finance

Wu, Yufei;Mahfouz, Mahmoud;Magazzeni, Daniele;Veloso, Manuela

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Abstract: The success of machine learning models is highly reliant on the quality and robustness of representations. The lack of attention on the robustness of representations may boost risks when using data-driven machine learning models for trading in the financial markets. In this paper, we focus on representations of the limit order book (LOB) data and discuss the opportunities and challenges of representing such data in an effective and robust manner. We analyse the issues associated with the commonly-used LOB representation for machine learning models from both theoretical and experimental perspectives. Based on this, we propose new LOB representation schemes to improve the performance and robustness of machine learning models and present a guideline for future research in this area.

Kabaivanov, S.;Zhelinski, V.;Zlatanov, B.

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Abstract: In this paper we generalize Hardy-Rogers maps in the context of coupled fixed points. We generalizes with the help of the obtained main theorem some known results about existence and uniqueness of market equilibrium in duopoly markets. We investigate some recent results about market equilibrium in duopoly markets with the help of the main theorem and we enrich them. We define a generalized response function including production and surpluses. Finally we illustrate a possible application of the main result in the investigation of market equilibrium, when the pay off functions are non differentiable.

Mahfouz, Mahmoud;Balch, Tucker;Veloso, Manuela;Mandic, Danilo

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Abstract: Continuous double auctions such as the limit order book employed by exchanges are widely used in practice to match buyers and sellers of a variety of financial instruments. In this work, we develop an agent-based model for trading in a limit order book and show (1) how opponent modelling techniques can be applied to classify trading agent archetypes and (2) how behavioural cloning can be used to imitate these agents in a simulated setting. We experimentally compare a number of techniques for both tasks and evaluate their applicability and use in real-world scenarios.

Bernhardt, Thomas;Qu, Ge

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Abstract: The income stability of a closed pooled annuity fund is studied. The focus is on quantifying the impact of inhomogeneous initial savings amounts on idiosyncratic longevity risk. Besides wealth inhomogeneity, the members of the pool are independent and identical copies of each other. We ignore systematic investment risk or mortality risk and define income stability as keeping the income within a specified tolerance of each member's initial income payment in a fixed proportion of future scenarios. For a given group of people with different savings amounts, we find an analytical expression that closely approximates the time for which the fund provides a stable income. Our main result uses this expression to determine if everyone benefits from pooling their funds with the whole group or how to split a cohort into different pooled annuity funds.

Kakushadze, Zura;Yu, Willie

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Abstract: We discuss how to build ETF risk models. Our approach anchors on i) first building a multilevel (non-)binary classification/taxonomy for ETFs, which is utilized in order to define the risk factors, and ii) then building the risk models based on these risk factors by utilizing the heterotic risk model construction of this https URL (for binary classifications) or general risk model construction of this https URL (for non-binary classifications). We discuss how to build an ETF taxonomy using ETF constituent data. A multilevel ETF taxonomy can also be constructed by appropriately augmenting and expanding well-built and granular third-party single-level ETF groupings.

Ma, Jingtang;Yang, Wensheng;Cui, Zhenyu

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Abstract: Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with Hurst parameter less than half. Due to the challenge that it is neither a semimartingale nor a Markov process, there is no unified method that not only applies to all rough volatility models, but also is computationally efficient. This paper proposes a semimartingale and continuous-time Markov chain (CTMC) approximation approach for the general class of rough stochastic local volatility (RSLV) models. In particular, we introduce the perturbed stochastic local volatility (PSLV) model as the semimartingale approximation for the RSLV model and establish its existence , uniqueness and Markovian representation. We propose a fast CTMC algorithm and prove its weak convergence. Numerical experiments demonstrate the accuracy and high efficiency of the method in pricing European, barrier and American options. Comparing with existing literature, a significant reduction in the CPU time to arrive at the same level of accuracy is observed.

Wang, Siyi;Yan, Xing;Zheng, Bangqi;Wang, Hu;Xu, Wangli;Peng, Nanbo;Wu, Qi

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Abstract: We design a system for risk-analyzing and pricing portfolios of non-performing consumer credit loans. The rapid development of credit lending business for consumers heightens the need for trading portfolios formed by overdue loans as a manner of risk transferring. However, the problem is nontrivial technically and related research is absent. We tackle the challenge by building a bottom-up architecture, in which we model the distribution of every single loan's repayment rate, followed by modeling the distribution of the portfolio's overall repayment rate. To address the technical issues encountered, we adopt the approaches of simultaneous quantile regression, R-copula, and Gaussian one-factor copula model. To our best knowledge, this is the first study that successfully adopts a bottom-up system for analyzing credit portfolio risks of consumer loans. We conduct experiments on a vast amount of data and prove that our methodology can be applied successfully in real business tasks.

Itkin, David;Larsson, Martin

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Abstract: We propose a unified approach to several problems in Stochastic Portfolio Theory (SPT), which is a framework for equity markets with a large number $d$ of stocks. Our approach combines open markets, where trading is confined to the top $N$ capitalized stocks as well as the market portfolio consisting of all $d$ assets, with a parametric family of models which we call hybrid Jacobi processes. We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use these results to study the associated financial markets. Their properties include (1) stability of the capital distribution curve and (2) unleveraged and explicit growth optimal strategies. The sub-class of rank Jacobi models are additionally shown to (3) serve as the worst-case model for a robust asymptotic growth problem under model ambiguity and (4) exhibit stability in the large-$d$ limit. Our definition of an open market is a relaxation of existing definitions which is essential to make the analysis tractable.

DiSilvio, Steven;Yu;Luo;Ozerov, Anthony

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Abstract: Figgie is a card game that approximates open-outcry commodities trading. We design strategies for Figgie and study their performance and the resulting market behavior. To do this, we develop a flexible agent-based discrete-event market simulation in which agents operating under our strategies can play Figgie. Our simulation builds upon previous work by simulating latencies between agents and the market in a novel and efficient way. The fundamentalist strategy we develop takes advantage of Figgie's unique notion of asset value, and is, on average, the profit-maximizing strategy in all combinations of agent strategies tested. We develop a strategy, the "bottom-feeder", which estimates value by observing orders sent by other agents, and find that it limits the success of fundamentalists. We also find that chartist strategies implemented, including one from the literature, fail by going into feedback loops in the small Figgie market. We further develop a bootstrap method for statistically comparing strategies in a zero-sum game. Our results demonstrate the wide-ranging applicability of agent-based discrete-event simulations in studying markets.

Coletta, Andrea;Prata, Matteo;Conti, Michele;Mercanti, Emanuele;Bartolini, Novella;Moulin, Aymeric;Vyetrenko, Svitlana;Balch, Tucker

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Abstract: Simulated environments are increasingly used by trading firms and investment banks to evaluate trading strategies before approaching real markets. Backtesting, a widely used approach, consists of simulating experimental strategies while replaying historical market scenarios. Unfortunately, this approach does not capture the market response to the experimental agents' actions. In contrast, multi-agent simulation presents a natural bottom-up approach to emulating agent interaction in financial markets. It allows to set up pools of traders with diverse strategies to mimic the financial market trader population, and test the performance of new experimental strategies. Since individual agent-level historical data is typically proprietary and not available for public use, it is difficult to calibrate multiple market agents to obtain the realism required for testing trading strategies. To addresses this challenge we propose a synthetic market generator based on Conditional Generative Adversarial Networks (CGANs) trained on real aggregate-level historical data. A CGAN-based "world" agent can generate meaningful orders in response to an experimental agent. We integrate our synthetic market generator into ABIDES, an open source simulator of financial markets. By means of extensive simulations we show that our proposal outperforms previous work in terms of stylized facts reflecting market responsiveness and realism.