Quantitative Finance

Saddier, Louis;Marsili, Matteo

doi: 10.48550/arxiv.2303.08867pmid: N/A

Abstract:The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include i) the square-root behaviour of the expected price variation with the total volume traded, ii) its crossover to a linear regime for small volumes, and iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from the over-estimation of order flows originating from meta-orders.

Manzano, Alberto;Ferro, Gonzalo;Leitao, Álvaro;Vázquez, Carlos;Gómez, Andrés

doi: 10.48550/arxiv.2303.06089pmid: N/A

Abstract:In this work we present an alternative methodology to the standard Quantum Accelerated Monte Carlo (QAMC) applied to derivatives pricing. Our pipeline benefits from the combination of a new encoding protocol, referred to as the direct encoding, and a amplitude estimation algorithm, the modified Real Quantum Amplitude Estimation (mRQAE) algorithm. On the one hand, the direct encoding prepares a quantum state which contains the information about the sign of the expected payoff. On the other hand, the mRQAE is able to read all the information contained in the quantum state. Although the procedure we describe is different from the standard one, the main building blocks are almost the same. Thus, all the extensive research that has been performed is still applicable. Moreover, we experimentally compare the performance of the proposed methodology against the standard QAMC employing a quantum emulator and show that we retain the speedups.

Lepak, Łukasz;Wawrzyński, Paweł

doi: 10.48550/arxiv.2303.16266pmid: N/A

Abstract:An increasing share of energy is produced from renewable sources by many small producers. The efficiency of those sources is volatile and, to some extent, random, exacerbating the problem of energy market balancing. In many countries, this balancing is done on the day-ahead (DA) energy markets. This paper considers automated trading on the DA energy market by a medium-sized prosumer. We model this activity as a Markov Decision Process and formalize a framework in which an applicable in real-life strategy can be optimized with off-line data. We design a trading strategy that is fed with the available environmental information that can impact future prices, including weather forecasts. We use state-of-the-art reinforcement learning (RL) algorithms to optimize this strategy. For comparison, we also synthesize simple parametric trading strategies and optimize them with an evolutionary algorithm. Results show that our RL-based strategy generates the highest market profits.

Junike, Gero

doi: 10.48550/arxiv.2303.16012pmid: N/A

Abstract:The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to specify two parameters: a truncation range for the density of the log-returns and a number of terms N to approximate the truncated density by a cosine series. How to choose the truncation range is already known. Here, we are able to find an explicit and useful bound for N as well for pricing and for the sensitivities, i.e., the Greeks Delta and Gamma, provided the density of the log-returns is smooth. We further show that the COS method has an exponential order of convergence when the density is smooth and decays exponentially. However, when the density is smooth and has heavy tails, as in the Finite Moment Log Stable model, the COS method does not have exponential order of convergence. Numerical experiments confirm the theoretical results.

Pabuccu, Hakan;Barbu, Adrian

doi: 10.48550/arxiv.2303.02223pmid: N/A

Abstract:Stock market and cryptocurrency forecasting is very important to investors as they aspire to achieve even the slightest improvement to their buy or hold strategies so that they may increase profitability. However, obtaining accurate and reliable predictions is challenging, noting that accuracy does not equate to reliability, especially when financial time-series forecasting is applied owing to its complex and chaotic tendencies. To mitigate this complexity, this study provides a comprehensive method for forecasting financial time series based on tactical input output feature mapping techniques using machine learning (ML) models. During the prediction process, selecting the relevant indicators is vital to obtaining the desired results. In the financial field, limited attention has been paid to this problem with ML solutions. We investigate the use of feature selection with annealing (FSA) for the first time in this field, and we apply the least absolute shrinkage and selection operator (Lasso) method to select the features from more than 1,000 candidates obtained from 26 technical classifiers with different periods and lags. Boruta (BOR) feature selection, a wrapper method, is used as a baseline for comparison. Logistic regression (LR), extreme gradient boosting (XGBoost), and long short-term memory (LSTM) are then applied to the selected features for forecasting purposes using 10 different financial datasets containing cryptocurrencies and stocks. The dependent variables consisted of daily logarithmic returns and trends. The mean-squared error for regression, area under the receiver operating characteristic curve, and classification accuracy were used to evaluate model performance, and the statistical significance of the forecasting results was tested using paired t-tests. Experiments indicate that the FSA algorithm increased the performance of ML models, regardless of problem type.

Raj, Manav;Berg, Justin;Seamans, Rob

doi: 10.48550/arxiv.2303.06217pmid: N/A

Abstract:The emergence of generative AI technologies, such as OpenAI's ChatGPT chatbot, has expanded the scope of tasks that AI tools can accomplish and enabled AI-generated creative content. In this study, we explore how disclosure regarding the use of AI in the creation of creative content affects human evaluation of such content. In a series of pre-registered experimental studies, we show that AI disclosure has no meaningful effect on evaluation either for creative or descriptive short stories, but that AI disclosure has a negative effect on evaluations for emotionally evocative poems written in the first person. We interpret this result to suggest that reactions to AI-generated content may be negative when the content is viewed as distinctly "human." We discuss the implications of this work and outline planned pathways of research to better understand whether and when AI disclosure may affect the evaluation of creative content.

Gaete-Morales, Carlos;Jöhrens, Julius;Heining, Florian;Schill, Wolf-Peter

doi: 10.1016/j.crsus.2024.100123pmid: N/A

Abstract:Various options are discussed to de-fossilize heavy-duty vehicles (HDV), including battery-electric vehicles (BEV), electric road systems (ERS), and indirect electrification via hydrogen fuel cells or e-fuels. We investigate their power sector implications in future scenarios of Germany with high renewable energy shares, using an open-source capacity expansion model and route-based truck traffic data. Power sector costs are lowest for flexibly charged BEV that also carry out vehicle-to-grid operations, and highest for e-fuels. If BEV and ERS-BEV are not optimally charged, power sector costs increase, but are still substantially lower than in scenarios with hydrogen or e-fuels. This is because indirect electrification is less energy efficient, which outweighs potential flexibility benefits. BEV and ERS-BEV favor solar photovoltaic energy, while hydrogen and e-fuels favor wind power and increase fossil electricity generation. Results remain qualitatively robust in sensitivity analyses.

Cherrat, El Amine;Raj, Snehal;Kerenidis, Iordanis;Shekhar, Abhishek;Wood, Ben;Dee, Jon;Chakrabarti, Shouvanik;Chen, Richard;Herman, Dylan;Hu, Shaohan;Minssen, Pierre;Shaydulin, Ruslan;Sun, Yue;Yalovetzky, Romina;Pistoia, Marco

doi: 10.22331/q-2023-11-29-1191pmid: N/A

Abstract:Quantum machine learning has the potential for a transformative impact across industry sectors and in particular in finance. In our work we look at the problem of hedging where deep reinforcement learning offers a powerful framework for real markets. We develop quantum reinforcement learning methods based on policy-search and distributional actor-critic algorithms that use quantum neural network architectures with orthogonal and compound layers for the policy and value functions. We prove that the quantum neural networks we use are trainable, and we perform extensive simulations that show that quantum models can reduce the number of trainable parameters while achieving comparable performance and that the distributional approach obtains better performance than other standard approaches, both classical and quantum. We successfully implement the proposed models on a trapped-ion quantum processor, utilizing circuits with up to $16$ qubits, and observe performance that agrees well with noiseless simulation. Our quantum techniques are general and can be applied to other reinforcement learning problems beyond hedging.

Bäuerle, Nicole;Mahayni, Antje

doi: 10.1016/j.ejor2024.01.022pmid: N/A

Abstract:We consider the classical multi-asset Merton investment problem under drift uncertainty, i.e. the asset price dynamics are given by geometric Brownian motions with constant but unknown drift coefficients. The investor assumes a prior drift distribution and is able to learn by observing the asset prize realizations during the investment horizon. While the solution of an expected utility maximizing investor with constant relative risk aversion (CRRA) is well known, we consider the optimization problem under risk and ambiguity preferences by means of the KMM (Klibanoff et al. (2005)) approach. Here, the investor maximizes a double certainty equivalent. The inner certainty equivalent is for given drift coefficient, the outer is based on a drift distribution. Assuming also a CRRA type ambiguity function, it turns out that the optimal strategy can be stated in terms of the solution without ambiguity preferences but an adjusted drift distribution. To the best of our knowledge an explicit solution method in this setting is new. We rely on some duality theorems to prove our statements. Based on our theoretical results, we are able to shed light on the impact of the prior drift distribution as well as the consequences of ambiguity preferences via the transfer to an adjusted drift distribution, i.e. we are able to explain the interaction of risk and ambiguity preferences. We compare our results with the ones in a pre-commitment setup where the investor is restricted to deterministic strategies. It turns out that (under risk and ambiguity aversion) an infinite investment horizon implies in both cases a maximin decision rule, i.e. the investor follows the worst (best) Merton fraction (over all realizations of it) if she is more (less) risk averse than a log-investor. We illustrate our findings with an extensive numerical study.

de Vilmarest, Joseph;Werge, Nicklas

doi: 10.48550/arxiv.2303.01855pmid: N/A

Abstract:In this paper, we address the problem of probabilistic forecasting using an adaptive volatility method rooted in classical time-varying volatility models and leveraging online stochastic optimization algorithms. These principles were successfully applied in the M6 forecasting competition under the team named AdaGaussMC. Our approach takes a unique path by embracing the Efficient Market Hypothesis (EMH) instead of trying to beat the market directly. We focus on evaluating the efficient market, emphasizing the importance of online forecasting in adapting to the dynamic nature of financial markets. The three key points of our approach are: (a) apply the univariate time-varying volatility model AdaVol, (b) obtain probabilistic forecasts of future returns, and (c) optimize the competition metrics using stochastic gradient-based algorithms. We contend that the simplicity of our approach contributes to its robustness and consistency. Remarkably, our performance in the M6 competition resulted in an overall 7th ranking, with a noteworthy 5th position in the forecasting task. This achievement, considering the perceived simplicity of our approach, underscores the efficacy of our adaptive volatility method in the realm of probabilistic forecasting.