Quantitative Finance
New submissions
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New submissions for Tue, 21 May 24
- [1] arXiv:2405.11329 [pdf, ps, other]
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Title: Risk-neutral valuation of options under arithmetic Brownian motionsComments: 19 pages, 4 figuresSubjects: Pricing of Securities (q-fin.PR); Mathematical Finance (q-fin.MF); Risk Management (q-fin.RM)
On April 22, 2020, the CME Group switched to Bachelier pricing for a group of oil futures options. The Bachelier model, or more generally the arithmetic Brownian motion (ABM), is not so widely used in finance, though. This paper provides the first comprehensive survey of options pricing under ABM. Using the risk-neutral valuation, we derive formulas for European options for three underlying types, namely an underlying that does not pay dividends, an underlying that pays a continuous dividend yield, and futures. Further, we derive Black-Scholes-Merton-like partial differential equations, which can in principle be utilized to price American options numerically via finite difference.
- [2] arXiv:2405.11392 [pdf, ps, other]
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Title: Deep Penalty Methods: A Class of Deep Learning Algorithms for Solving High Dimensional Optimal Stopping ProblemsSubjects: Mathematical Finance (q-fin.MF); Computational Finance (q-fin.CP)
We propose a deep learning algorithm for high dimensional optimal stopping problems. Our method is inspired by the penalty method for solving free boundary PDEs. Within our approach, the penalized PDE is approximated using the Deep BSDE framework proposed by \cite{weinan2017deep}, which leads us to coin the term "Deep Penalty Method (DPM)" to refer to our algorithm. We show that the error of the DPM can be bounded by the loss function and $O(\frac{1}{\lambda})+O(\lambda h) +O(\sqrt{h})$, where $h$ is the step size in time and $\lambda$ is the penalty parameter. This finding emphasizes the need for careful consideration when selecting the penalization parameter and suggests that the discretization error converges at a rate of order $\frac{1}{2}$. We validate the efficacy of the DPM through numerical tests conducted on a high-dimensional optimal stopping model in the area of American option pricing. The numerical tests confirm both the accuracy and the computational efficiency of our proposed algorithm.
- [3] arXiv:2405.11444 [pdf, other]
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Title: Adaptive Optimal Market Making Strategies with Inventory Liquidation CosComments: A preprint of this paper was distributed under the title of "Market Making with Stochastic Liquidity Demand: Simultaneous Order Arrival and Price Change Forecasts". The present paper extends the results in the referred preprint, which will remain as an unpublished manuscriptSubjects: Trading and Market Microstructure (q-fin.TR)
A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand's randomness affects the optimal placement strategy. We also allow the price process to follow general dynamics without any Brownian or martingale assumption as is commonly adopted in the literature. The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using the actual flow of orders in the LOB. Our adaptive optimal strategies outperform the non-adaptive strategy and those that quote limit orders at a fixed distance from the midprice.
- [4] arXiv:2405.11455 [pdf, other]
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Title: Impact Analysis of the Chesa Boudin AdministrationAuthors: Jordan G. Taqi-EddinSubjects: General Economics (econ.GN)
Claims of soft-handed prosecutorial policies and increases in crime were precipitating factors in the removal of Chesa Boudin as district attorney of the city and county of San Francisco. However, little research has been conducted to empirically investigate the veracity of these indictments on the former district attorney. Using regression discontinuity design (RDD), I find that the Boudin administration led to a 36\% and 21\% reduction in monthly prosecutions and convictions respectively for all crimes. Moreover, his tenure increased monthly successful case diversions by 58\%. When only looking at violent crimes during this period, the SFDA's office saw a 36\% decrease, 7\% decrease, and 47\% increase in monthly prosecutions, convictions, and successful case diversions respectively. Although, the decrease in monthly convictions was not statistically significant for the violent crimes subset. Additionally, I did identify a potentially causal relationship between lower numbers of prosecutions and higher levels of criminal activity, however, such findings did not meet the standard for statistical significance. Finally, I conclude that using machine learning algorithms, such as neural networks and K-nearest neighbors, in place of ordinary least squares regression for the estimation of the reduced form equation possibly may decrease the size of the standard errors of the parameters in the structural equation. However, future research needs to be conducted in this space to corroborate these initially promising findings.
- [5] arXiv:2405.11686 [pdf, other]
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Title: Exploiting Distributional Value Functions for Financial Market Valuation, Enhanced Feature Creation and Improvement of Trading AlgorithmsAuthors: Colin D. GrabComments: 22 pages, 13 figuresSubjects: Statistical Finance (q-fin.ST); Computational Finance (q-fin.CP)
While research of reinforcement learning applied to financial markets predominantly concentrates on finding optimal behaviours, it is worth to realize that the reinforcement learning returns $G_t$ and state value functions themselves are of interest and play a pivotal role in the evaluation of assets. Instead of focussing on the more complex task of finding optimal decision rules, this paper studies and applies the power of distributional state value functions in the context of financial market valuation and machine learning based trading algorithms. Accurate and trustworthy estimates of the distributions of $G_t$ provide a competitive edge leading to better informed decisions and more optimal behaviour. Herein, ideas from predictive knowledge and deep reinforcement learning are combined to introduce a novel family of models called CDG-Model, resulting in a highly flexible framework and intuitive approach with minimal assumptions regarding underlying distributions. The models allow seamless integration of typical financial modelling pitfalls like transaction costs, slippage and other possible costs or benefits into the model calculation. They can be applied to any kind of trading strategy or asset class. The frameworks introduced provide concrete business value through their potential in market valuation of single assets and portfolios, in the comparison of strategies as well as in the improvement of market timing. They can positively impact the performance and enhance the learning process of existing or new trading algorithms. They are of interest from a scientific point-of-view and open up multiple areas of future research. Initial implementations and tests were performed on real market data. While the results are promising, applying a robust statistical framework to evaluate the models in general remains a challenge and further investigations are needed.
- [6] arXiv:2405.12041 [pdf, ps, other]
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Title: Earthquakes and the wealth of nations: The cases of Chile and New ZealandSubjects: General Economics (econ.GN)
The consequences of natural disasters, such as earthquakes, are evident: death, coordination problems, destruction of infrastructure, and displacement of population. However, according to empirical research, the impact of a natural disaster on economic activity is mixed. Natural disasters could have significant economic effects, especially in developing economies. This is particularly important for highly seismic countries such as Chile and New Zealand. This paper contributes to the literature on natural disasters and economic development by analyzing the cases of two affected regions within these countries in the wake of major earthquakes experienced during 2010-2011: Maule (Chile) and Canterbury (New Zealand). We examine the impact of natural disasters on GDP per capita by applying the synthetic control method. Using the synthetic approach, we assess the effects of these two earthquakes by building counterfactuals to compare their recovery trajectories. We find that Chile and New Zealand experienced opposite economic effects. The Canterbury region grew 10% more in three years than its synthetic counterfactual without the earthquake, while the Maule region declined by 5%. We build synthetic controls at a regional and economic-sector level, looking at aggregated and sectoral effects. The difference in institutions, such as property rights and the large amount of government spending given for reconstruction after the New Zealand earthquake relative to Chile's, help to explain the difference in outcomes.
- [7] arXiv:2405.12154 [pdf, ps, other]
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Title: Risk, utility and sensitivity to large lossesSubjects: Risk Management (q-fin.RM); Mathematical Finance (q-fin.MF)
Risk and utility functionals are fundamental building blocks in economics and finance. In this paper we investigate under which conditions a risk or utility functional is sensitive to the accumulation of losses in the sense that any sufficiently large multiple of a position that exposes an agent to future losses has positive risk or negative utility. We call this property sensitivity to large losses and provide necessary and sufficient conditions thereof that are easy to check for a very large class of risk and utility functionals. In particular, our results do not rely on convexity and can therefore also be applied to most examples discussed in the recent literature, including (non-convex) star-shaped risk measures or S-shaped utility functions encountered in prospect theory. As expected, Value at Risk generally fails to be sensitive to large losses. More surprisingly, this is also true of Expected Shortfall. By contrast, expected utility functionals as well as (optimized) certainty equivalents are proved to be sensitive to large losses for many standard choices of concave and nonconcave utility functions, including $S$-shaped utility functions. We also show that Value at Risk and Expected Shortfall become sensitive to large losses if they are either properly adjusted or if the property is suitably localized.
Cross-lists for Tue, 21 May 24
- [8] arXiv:2405.11431 (cross-list from cs.LG) [pdf, other]
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Title: Review of deep learning models for crypto price prediction: implementation and evaluationSubjects: Machine Learning (cs.LG); Statistical Finance (q-fin.ST); Machine Learning (stat.ML)
There has been much interest in accurate cryptocurrency price forecast models by investors and researchers. Deep Learning models are prominent machine learning techniques that have transformed various fields and have shown potential for finance and economics. Although various deep learning models have been explored for cryptocurrency price forecasting, it is not clear which models are suitable due to high market volatility. In this study, we review the literature about deep learning for cryptocurrency price forecasting and evaluate novel deep learning models for cryptocurrency stock price prediction. Our deep learning models include variants of long short-term memory (LSTM) recurrent neural networks, variants of convolutional neural networks (CNNs), and the Transformer model. We evaluate univariate and multivariate approaches for multi-step ahead predicting of cryptocurrencies close-price. Our results show that the univariate LSTM model variants perform best for cryptocurrency predictions. We also carry out volatility analysis on the four cryptocurrencies which reveals significant fluctuations in their prices throughout the COVID-19 pandemic. Additionally, we investigate the prediction accuracy of two scenarios identified by different training sets for the models. First, we use the pre-COVID-19 datasets to model cryptocurrency close-price forecasting during the early period of COVID-19. Secondly, we utilise data from the COVID-19 period to predict prices for 2023 to 2024.
- [9] arXiv:2405.11730 (cross-list from cs.LG) [pdf, ps, other]
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Title: Degree of Irrationality: Sentiment and Implied Volatility SurfaceComments: 21 pages, 8 figuresSubjects: Machine Learning (cs.LG); General Finance (q-fin.GN)
In this study, we constructed daily high-frequency sentiment data and used the VAR method to attempt to predict the next day's implied volatility surface. We utilized 630,000 text data entries from the East Money Stock Forum from 2014 to 2023 and employed deep learning methods such as BERT and LSTM to build daily market sentiment indicators. By applying FFT and EMD methods for sentiment decomposition, we found that high-frequency sentiment had a stronger correlation with at-the-money (ATM) options' implied volatility, while low-frequency sentiment was more strongly correlated with deep out-of-the-money (DOTM) options' implied volatility. Further analysis revealed that the shape of the implied volatility surface contains richer market sentiment information beyond just market panic. We demonstrated that incorporating this sentiment information can improve the accuracy of implied volatility surface predictions.
Replacements for Tue, 21 May 24
- [10] arXiv:2009.01676 (replaced) [pdf, other]
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Title: Automated Market Makers for Decentralized Finance (DeFi)Authors: Yongge WangComments: 14 pages, 9 figuresSubjects: Trading and Market Microstructure (q-fin.TR); Discrete Mathematics (cs.DM); Computer Science and Game Theory (cs.GT)
- [11] arXiv:2104.14412 (replaced) [pdf, ps, other]
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Title: Nonparametric Test for Volatility in Clustered Multiple Time SeriesSubjects: Statistical Finance (q-fin.ST); Methodology (stat.ME)
- [12] arXiv:2110.05608 (replaced) [pdf, ps, other]
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Title: Tiebout sorting in online communitiesSubjects: General Economics (econ.GN)
- [13] arXiv:2202.07610 (replaced) [pdf, other]
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Title: $ρ$-arbitrage and $ρ$-consistent pricing for star-shaped risk measuresSubjects: Mathematical Finance (q-fin.MF)
- [14] arXiv:2403.03612 (replaced) [pdf, ps, other]
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Title: Using the Dual-Privacy Framework to Understand Consumers' Perceived Privacy Violations Under Different Firm Practices in Online AdvertisingSubjects: General Economics (econ.GN)
- [15] arXiv:2405.03496 (replaced) [pdf, ps, other]
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Title: Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static LiquiditySubjects: Trading and Market Microstructure (q-fin.TR)
- [16] arXiv:2405.08159 (replaced) [pdf, ps, other]
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Title: Large increases in public R&D investment are needed to avoid declines of US agricultural productivityComments: Main text: 19 pages, 4 figures. Supplementary material: 47 pages, 20 figures, 13 tablesSubjects: General Economics (econ.GN)
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