Volatility Modeling

Evaluating the resilience of ESG investments in European Markets during turmoil periods ArXiv ID: 2501.03269 “View on arXiv” Authors: Unknown Abstract This study investigates the resilience of Environmental, Social, and Governance (ESG) investments during periods of financial instability, comparing them with traditional equity indices across major European markets-Germany, France, and Italy. Using daily returns from October 2021 to February 2024, the analysis explores the effects of key global disruptions such as the Covid-19 pandemic and the Russia-Ukraine conflict on market performance. A mixture of two generalised normal distributions (MGND) and EGARCH-in-mean models are used to identify periods of market turmoil and assess volatility dynamics. The findings indicate that during crises, ESG investments present higher volatility in Germany and Italy than in France. Despite some regional variations, ESG portfolios demonstrate greater resilience compared to traditional ones, offering potential risk mitigation during market shocks. These results underscore the importance of integrating ESG factors into long-term investment strategies, particularly in the face of unpredictable financial turmoil. ...

Volatility-Volume Order Slicing via Statistical Analysis ArXiv ID: 2412.12482 “View on arXiv” Authors: Unknown Abstract This paper addresses the challenges faced in large-volume trading, where executing substantial orders can result in significant market impact and slippage. To mitigate these effects, this study proposes a volatility-volume-based order slicing strategy that leverages Exponential Weighted Moving Average and Markov Chain Monte Carlo simulations. These methods are used to dynamically estimate future trading volumes and price ranges, enabling traders to adapt their strategies by segmenting order execution sizes based on these predictions. Results show that the proposed approach improves trade execution efficiency, reduces market impact, and offers a more adaptive solution for volatile market conditions. The findings have practical implications for large-volume trading, providing a foundation for further research into adaptive execution strategies. ...

Computing the SSR ArXiv ID: 2406.16131 “View on arXiv” Authors: Unknown Abstract The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion setting, it is well-known that the short-term limit of the SSR is 2; a corollary of our results is that this limit is $H+3/2$ where $H$ is the Hurst exponent of the volatility process. The general formula for the SSR simplifies and becomes particularly tractable in the affine forward variance case. We explain the qualitative behavior of the SSR with respect to the shape of the forward variance curve, and thus also path-dependence of the SSR. ...

Prediction of Cryptocurrency Prices through a Path Dependent Monte Carlo Simulation ArXiv ID: 2405.12988 “View on arXiv” Authors: Unknown Abstract In this paper, our focus lies on the Merton’s jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of methodologies. We adopt an approach that involves implementing different drift, volatility, and jump terms within the model through various machine learning techniques, traditional methods, and statistical methods on price-volume data. Additionally, we introduce a path-dependent Monte Carlo simulation to model cryptocurrency prices, taking into account the volatility and unexpected jumps in prices. ...

Introducing the $σ$-Cell: Unifying GARCH, Stochastic Fluctuations and Evolving Mechanisms in RNN-based Volatility Forecasting ArXiv ID: 2309.01565 “View on arXiv” Authors: Unknown Abstract This paper introduces the $σ$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $σ$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating domain knowledge with neural networks. ...

The Implied Views of Bond Traders on the Spot Equity Market ArXiv ID: 2306.16522 “View on arXiv” Authors: Unknown Abstract This study delves into the temporal dynamics within the equity market through the lens of bond traders. Recognizing that the riskless interest rate fluctuates over time, we leverage the Black-Derman-Toy model to trace its temporal evolution. To gain insights from a bond trader’s perspective, we focus on a specific type of bond: the zero-coupon bond. This paper introduces a pricing algorithm for this bond and presents a formula that can be used to ascertain its real value. By crafting an equation that juxtaposes the theoretical value of a zero-coupon bond with its actual value, we can deduce the risk-neutral probability. It is noteworthy that the risk-neutral probability correlates with variables like the instantaneous mean return, instantaneous volatility, and inherent upturn probability in the equity market. Examining these relationships enables us to discern the temporal shifts in these parameters. Our findings suggest that the mean starts at a negative value, eventually plateauing at a consistent level. The volatility, on the other hand, initially has a minimal positive value, peaks swiftly, and then stabilizes. Lastly, the upturn probability is initially significantly high, plunges rapidly, and ultimately reaches equilibrium. ...

A Multifractal Model of Asset Returns ArXiv ID: ssrn-78588 “View on arXiv” Authors: Unknown Abstract This paper presents the “multifractal model of asset returns” (“MMAR”), based upon the pioneering research into multifractal measures by Man Keywords: Multifractal Models, Asset Returns, Stochastic Processes, Time Series Analysis, Volatility Modeling, Equity Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 6.0/10 Quadrant: Holy Grail Why: The paper employs advanced mathematical concepts like multifractal measures, long-dependence, and scaling laws, indicating high mathematical complexity. It also discusses empirical implications, comparisons with GARCH/FIGARCH, and references companion empirical work, showing substantial empirical rigor. flowchart TD Goal["Research Goal:<br>Create model for asset return volatility<br>(MMAR)"] --> Inputs["Data/Input:<br>Equity index returns<br>High-frequency time series"] Inputs --> Method["Key Method:<br>Multifractal measures &<br>stochastic cascade process"] Method --> Comp["Computational Process:<br>Model calibration &<br>time-scale analysis"] Comp --> Findings["Key Findings/Outcomes:<br>1. Captures heavy tails<br>2. Explains volatility clustering<br>3. Superior to GARCH models"] Findings --> Final["Conclusion:<br>MMAR accurately describes<br>multifractal nature of markets"]