GARCH

Combining Deep Learning and GARCH Models for Financial Volatility and Risk Forecasting ArXiv ID: 2310.01063 “View on arXiv” Authors: Unknown Abstract In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated Recurrent Unit (GRU) networks, whereas four different specifications are used as the GARCH component: standard GARCH, EGARCH, GJR-GARCH and APARCH. Models are tested using daily logarithmic returns on the S&P 500 index as well as gold price Bitcoin prices, with the three assets representing quite distinct volatility dynamics. As the main volatility estimator, also underlying the target function of our hybrid models, we use the price-range-based Garman-Klass estimator, modified to incorporate the opening and closing prices. Volatility forecasts resulting from the hybrid models are employed to evaluate the assets’ risk using the Value-at-Risk (VaR) and Expected Shortfall (ES) at two different tolerance levels of 5% and 1%. Gains from combining the GARCH and GRU approaches are discussed in the contexts of both the volatility and risk forecasts. In general, it can be concluded that the hybrid solutions produce more accurate point volatility forecasts, although it does not necessarily translate into superior VaR and ES forecasts. ...

Sizing Strategies for Algorithmic Trading in Volatile Markets: A Study of Backtesting and Risk Mitigation Analysis ArXiv ID: 2309.09094 “View on arXiv” Authors: Unknown Abstract Backtest is a way of financial risk evaluation which helps to analyze how our trading algorithm would work in markets with past time frame. The high volatility situation has always been a critical situation which creates challenges for algorithmic traders. The paper investigates different models of sizing in financial trading and backtest to high volatility situations to understand how sizing models can lower the models of VaR during crisis events. Hence it tries to show that how crisis events with high volatility can be controlled using short and long positional size. The paper also investigates stocks with AR, ARIMA, LSTM, GARCH with ETF data. ...

Real-time VaR Calculations for Crypto Derivatives in kdb+/q ArXiv ID: 2309.06393 “View on arXiv” Authors: Unknown Abstract Cryptocurrency market is known for exhibiting significantly higher volatility than traditional asset classes. Efficient and adequate risk calculation is vital for managing risk exposures in such market environments where extreme price fluctuations occur in short timeframes. The objective of this thesis is to build a real-time computation workflow that provides VaR estimates for non-linear portfolios of cryptocurrency derivatives. Many researchers have examined the predictive capabilities of time-series models within the context of cryptocurrencies. In this work, we applied three commonly used models - EMWA, GARCH and HAR - to capture and forecast volatility dynamics, in conjunction with delta-gamma-theta approach and Cornish-Fisher expansion to crypto derivatives, examining their performance from the perspectives of calculation efficiency and accuracy. We present a calculation workflow which harnesses the information embedded in high-frequency market data and the computation simplicity inherent in analytical estimation procedures. This workflow yields reasonably robust VaR estimates with calculation latencies on the order of milliseconds. ...

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. ...