Quantitative Finance

Ararat, Çağın;Feinstein, Zachary

doi: N/Apmid: N/A

Abstract: Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of set-valued functionals in the recent literature. There are two possible extensions of scalar backward stochastic differential equations for the set-valued framework: (1) backward stochastic differential inclusions, which evaluate the risk dynamics on the selectors of acceptable capital allocations; or (2) set-valued backward stochastic differential equations, which evaluate the risk dynamics on the full set of acceptable capital allocations as a singular object. In this work, the discrete time setting is investigated with difference inclusions and difference equations in order to provide insights for such differential representations for set-valued dynamic risk measures in continuous time.

Kardaras, Constantinos;Ruf, Johannes

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Abstract: We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale part in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller information market. Via use of a Bayesian filtering approach, we demonstrate the exact mechanism of how updates on the possible class of models under less information result in the strict supermartingale property of projections of such deflators. Finally, we demonstrate that these projections are unable to span all possible local martingale deflators in the smaller information market, by investigating a situation where market completeness is not retained under filtration shrinkage.

Bayraktar, Erhan;Dolinskyi, Leonid;Dolinsky, Yan

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Abstract: In this paper we study utility maximization with proportional transaction costs. Assuming extended weak convergence of the underlying processes we prove the convergence of the corresponding utility maximization problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in [1] and the Meyer--Zheng topology introduced in [24].

Hanifan, Henry;Cartlidge, John

doi: 10.5220/0008973700820093pmid: N/A

Abstract: We explore the competitive effects of reaction time of automated trading strategies in simulated financial markets containing a single exchange with public limit order book and continuous double auction matching. A large body of research conducted over several decades has been devoted to trading agent design and simulation, but the majority of this work focuses on pricing strategy and does not consider the time taken for these strategies to compute. In real-world financial markets, speed is known to heavily influence the design of automated trading algorithms, with the generally accepted wisdom that faster is better. Here, we introduce increasingly realistic models of trading speed and profile the computation times of a suite of eminent trading algorithms from the literature. Results demonstrate that: (a) trading performance is impacted by speed, but faster is not always better; (b) the Adaptive-Aggressive (AA) algorithm, until recently considered the most dominant trading strategy in the literature, is outperformed by the simplistic Shaver (SHVR) strategy - shave one tick off the current best bid or ask - when relative computation times are accurately simulated.

Becker, Sebastian;Cheridito, Patrick;Jentzen, Arnulf

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Abstract: In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors.

Černý, Aleš;Ruf, Johannes

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Abstract: The paper introduces a simple way of recording and manipulating general stochastic processes without explicit reference to a probability measure. In the new calculus, operations traditionally presented in a measure-specific way are instead captured by tracing the behaviour of jumps (also when no jumps are physically present). The calculus is fail-safe in that, under minimal assumptions, all informal calculations yield mathematically well-defined stochastic processes. The calculus is also intuitive as it allows the user to pretend all jumps are of compound Poisson type. The new calculus is very effective when it comes to computing drifts and expected values that possibly involve a change of measure. Such drift calculations yield, for example, partial integro-differential equations, Hamilton-Jacobi-Bellman equations, Feynman-Kac formulae, or exponential moments needed in numerous applications. We provide several illustrations of the new technique, among them a novel result on the Margrabe option to exchange one defaultable asset for another.

Chuan, Yijian;Wu, Lan

doi: N/Apmid: N/A

Abstract: Cross-sectional "Information Coefficient" (IC) is a widely and deeply accepted measure in portfolio management. The paper gives an insight into IC in view of high-dimensional directional statistics: IC is a linear operator on the components of a centralizing-unitizing standardized random vector of next-period cross-sectional returns. Our primary research first clearly defines IC with the high-dimensional directional statistics, discussing its first two moments. We derive the closed-form expressions of the directional statistics' covariance matrix and IC's variance in a homoscedastic condition. Also, we solve the optimization of IC's maximum expectation and minimum variance. Simulation intuitively characterizes the standardized directional statistics and IC's p.d.f.. The empirical analysis of the Chinese stock market uncovers interesting facts about the standardized vectors of cross-sectional returns and helps obtain the time series of the measure in the real market. The paper discovers a potential application of directional statistics in finance, proves explicit results of the projected normal distribution, and reveals IC's nature.

James, Nick;Menzies, Max;Chan, Jennifer

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Abstract: This paper introduces new methods for analysing the extreme and erratic behaviour of time series to evaluate the impact of COVID-19 on cryptocurrency market dynamics. Across 51 cryptocurrencies, we examine extreme behaviour through a study of distribution extremities, and erratic behaviour through structural breaks. First, we analyse the structure of the market as a whole and observe a reduction in self-similarity as a result of COVID-19, particularly with respect to structural breaks in variance. Second, we compare and contrast these two behaviours, and identify individual anomalous cryptocurrencies. USDT and TUSD are consistent outliers with respect to their returns, while HOT, NEXO, MKR and XEM are frequently observed as anomalous with respect to both behaviours and time. Even among a market known as consistently volatile, this identifies individual cryptocurrencies that behave most irregularly in their extreme and erratic behaviour and shows these were more affected during the COVID-19 market crisis.

Fang, Jie;Xia, Shutao;Lin, Jianwu;Xia, Zhikang;Liu, Xiang;Jiang, Yong

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Abstract: Genetic programming (GP) is the state-of-the-art in financial automated feature construction task. It employs reverse polish expression to represent features and then conducts the evolution process. However, with the development of deep learning, more powerful feature extraction tools are available. This paper proposes Alpha Discovery Neural Network (ADNN), a tailored neural network structure which can automatically construct diversified financial technical indicators based on prior knowledge. We mainly made three contributions. First, we use domain knowledge in quantitative trading to design the sampling rules and object function. Second, pre-training and model pruning has been used to replace genetic programming, because it can conduct more efficient evolution process. Third, the feature extractors in ADNN can be replaced by different feature extractors and produce different functions. The experiment results show that ADNN can construct more informative and diversified features than GP, which can effectively enriches the current factor pool. The fully-connected network and recurrent network are better at extracting information from the financial time series than the convolution neural network. In real practice, features constructed by ADNN can always improve multi-factor strategies' revenue, sharpe ratio, and max draw-down, compared with the investment strategies without these factors.

Kokabisaghi, Somayeh;Ezazi, Mohammadesmaeil;Tehrani, Reza;Yaghoubi, Nourmohammad

doi: N/Apmid: N/A

Abstract: In this paper, we model the impact of oil price volatility on Tehranstock and industry indices in two periods of international sanctions and post-sanction. To analyse the purpose of study, we use Feed-forward neural net-works. The period of study is from 2008 to 2018 that is split in two periods during international energy sanction and post-sanction. The results show that Feed-forward neural networks perform well in predicting stock market and industry, which means oil price volatility has a significant impact on stock and industry market indices. During post-sanction and global financial crisis, the model performs better in predicting industry index. Additionally, oil price-stock market index prediction performs better in the period of international sanctions. Herein, these results are, up to some extent, important for financial market analysts and policy makers to understand which factors and when influence the financial market, especially in an oil-dependent country such asIran with uncertainty in the international politics. Keywords: Feed-forward neural networks,Industry index,International energy sanction,Oil price volatility,Tehran stock index