Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 5

WP(13/2024)449. The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models

Authors: Natalia Roszyk, Ślepaczuk Robert
Predicting the S&P 500 index's volatility is crucial for investors and financial analysts as it helps in assessing market risk and making informed investment decisions. Volatility represents the level of uncertainty or risk related to the siz…

WP449. The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models

Predicting the S&P 500 index's volatility is crucial for investors and financial analysts as it helps in assessing market risk and making informed investment decisions. Volatility represents the level of uncertainty or risk related to the size of changes in a security's value, making it an essential indicator for financial planning. This study explores four methods to improve the accuracy of volatility forecasts for the S&P 500: the established GARCH model, known for capturing historical volatility patterns; an LSTM network that utilizes past volatility and log returns; a hybrid LSTM-GARCH model that combines the strengths of both approaches; and an advanced version of the hybrid model that also factors in the VIX index to gauge market sentiment. This analysis is based on a daily dataset that includes data for S&P 500 and VIX index, covering the period from January 3, 2000, to December 21, 2023. Through rigorous testing and comparison, we found that machine learning approaches, particularly the hybrid LSTM models, significantly outperform the traditional GARCH model. The inclusion of the VIX index in the hybrid model further enhances its forecasting ability by incorporating real-time market sentiment. The results of this study offer valuable insights for achieving more accurate volatility predictions, enabling better risk management and strategic investment decisions in the volatile environment of the S&P 500.


DOI: https://doi.org/10.33138/2957-0506.2024.13.449
Natalia Roszyk, Ślepaczuk Robert
volatility forecasting LSTM-GARCH S&P 500 index hybrid forecasting models VIX index machine learning financial time series analysis walk-forward process hyperparameters tuning deep learning recurrent neural networks

WP(3/2015)151. Bivariate GARCH models for single asset returns

Authors: Skoczylas Tomasz
In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This app…

WP151. Bivariate GARCH models for single asset returns

In this paper an alternative approach to modelling and forecasting single asset returns volatility is presented. A new, bivariate, flexible framework, which may be considered as a development of single-equation ARCH-type models, is proposed. This approach focuses on joint distribution of returns and observed volatility, measured by Garman-Klass variance estimator, and it enables to examine simultaneous dependencies between them. Proposed models are compared with benchmark GARCH and range-based GARCH (RGARCH) models in terms of prediction accuracy. All models are estimated with maximum likelihood method, using time series of EUR/PLN spot rate quotations and WIG20 index. Results are very encouraging especially for foreasting Value-at-Risk. Bivariate models achieved lesser rates of VaR exception, as well as lower coverage tests statistics, without being more conservative than its single-equation counterparts, as their forecasts errors measures are rather similar.


Skoczylas Tomasz
bivariate volatility models joint distribution range-based volatility estimators Garman-Klass estimator observed volatility volatility modelling GARCH leverage Value-at-Risk volatility forecasting

WP(6/2014)123. Modeling volatility with Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity model

Authors: Skoczylas Tomasz
In this paper a new ARCH-type volatility model is proposed. The Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity (RHARCH) model draws inspiration from Heterogeneous Autoregressive Conditional Heteroskedasticity presented by Mul…

WP123. Modeling volatility with Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity model

In this paper a new ARCH-type volatility model is proposed. The Range-based Heterogeneous Autoregressive Conditional Heteroskedasticity (RHARCH) model draws inspiration from Heterogeneous Autoregressive Conditional Heteroskedasticity presented by Muller et al. (1995), but employs more efficient, range-based volatility estimators instead of simple squared returns in conditional variance equation. In the first part of this research range-based volatility estimators (such as Parkinson, or Garman-Klass estimators) are reviewed, followed by derivation of the RHARCH model. In the second part of this research the RHARCH model is compared with selected ARCH-type models with particular emphasis on forecasting accuracy. All models are estimated using data containing EURPLN spot rate quotation. Results show that RHARCH model often outperforms return-based models in terms of predictive abilities in both in-sample and out-of-sample periods. Also properties of standardized residuals are very encouraging in case of the RHARCH model.


Skoczylas Tomasz
volatility modelling volatility forecasting ARCH range-based volatility estimators heterogeneity of volatility

WP(13/2009)23. High-Frequency and Model-Free Volatility Estimators

Authors: Ślepaczuk Robert, Zakrzewski Grzegorz
This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regard to modeling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where th…

WP23. High-Frequency and Model-Free Volatility Estimators

This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regard to modeling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where the concept of volatility estimators (consistent, unbiased and the most efficient) is of crucial concern. Our intention was to find the best estimator of true volatility taking into account the latest investigations in finance literature. Basing on the methodology presented in Parkinson (1980), Garman and Klass (1980), Rogers and Satchell (1991), Yang and Zhang (2000), Andersen et al. (1997, 1998, 1999a, 199b), Hansen and Lunde (2005, 2006b) and Martens (2007), we computed the various model-free volatility estimators and compared them with classical volatility estimator, most often used in financial models. In order to reveal the information set hidden in high-frequency data, we utilized the concept of realized volatility and realized range. Calculating our estimator, we carefully focused on - (the interval used in calculation), n (the memory of the process) and q (scaling factor for scaled estimators). Our results revealed that the appropriate selection of - and n plays a crucial role when we try to answer the question concerning the estimator efficiency, as well as its accuracy. Having nine estimators of volatility, we found that for optimal n (measured in days) and - (in minutes) we obtain the most efficient estimator. Our findings confirmed that the best estimator should include information contained not only in closing prices but in the price range as well (range estimators). What is more important, we focused on the properties of the formula itself, independently of the interval used, comparing the estimator with the same, n and q parameter. We observed that the formula of volatility estimator is not as important as the process of selection of the optimal parameter n or. Finally, we focused on the asymmetry between market turmoil and adjustments of volatility. Next, we put stress on the implications of our results for well-known financial models which utilize classical volatility estimator as the main input variable.


Ślepaczuk Robert, Zakrzewski Grzegorz
financial market volatility high-frequency financial data realized volatility and correlation volatility forecasting microstructure bias the opening jump effect the bid-ask bounce autocovariance bias daily patterns of volatility emerging markets

WP(11/2009)21. Emerging versus developed volatility indices. The comparison of VIW20 and VIX indices.

Authors: Ślepaczuk Robert, Zakrzewski Grzegorz
Modeling of financial markets volatility is one of the most significant issues of contemporary finance, especially with regard to analyzing high-frequency data. Accurate quantification and forecast of volatility are of immense importance in risk mana…

WP21. Emerging versus developed volatility indices. The comparison of VIW20 and VIX indices.

Modeling of financial markets volatility is one of the most significant issues of contemporary finance, especially with regard to analyzing high-frequency data. Accurate quantification and forecast of volatility are of immense importance in risk management (VaR models, stress testing and worst-case scenario), models of capital market and options valuation techniques. What we show in this paper is the methodology for calculating volatility index for Polish capital market (VIW20 - index anticipating expected volatility of WIG20 index). The methods presented are based on VIX index (VIX White Paper, 2003) and enriched with necessary modifications corresponding to the character of Polish options market. Quoted on CBOE, VIX index is currently known as the best measure of capital investment risk perfectly illustrating the level of fear and emotions of market participants. The conception of volatility index is based on the combination of realized volatility and implied volatility which, using methodology of Derman et al. (1999) and reconstructing volatility surface, reflects both volatility smile as well as its term structure. The research is carried out using high-frequency data (i.e. tick data) for index options on WIG20 index for the period November 2003 - May 2007, in other words, starting with the introduction of options by Warsaw Stock Exchange. All additional simulations are carried out using data gathered in years 1998-2008. Having analyzed VIW20 index in detail, we observed its characteristic behavior during the periods of strong market turmoils. What we also present is the analysis of the influence of VIW20 and VIX index-based instruments both on construction of minimum risk portfolio and on the quality of derivatives portfolio management in which volatility risk and liquidity risk play a key role. The main objective of this paper is to provide foundations for introducing appropriate volatility indices and volatility-based derivatives. This is done with paying attention to crucial methodology changes, necessary if one considers strong markets inefficiencies in emerging countries. As the introduction of appropriate instruments will enable active management of risks that are unhedgable nowadays it will significantly contribute to the development of the given markets in the course of time. In the summary we additionally point to the benefits Warsaw Stock Exchange might obtain from, being one of the few emerging markets possessing appropriately quantified investment risk as well as derivatives to manage it.


Ślepaczuk Robert, Zakrzewski Grzegorz
financial market volatility high-frequency data realized volatility realized range implied and historical volatility volatility forecasting option pricing models investment strategies portfolio optimization
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