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Bayesian Pricing of an European Call Option Using a GARCH Model with Asymmetries

100%
Osiewalski J., Pipień M., Akademia Ekonomiczna w Krakowie K. E.
Acta Universitatis Lodziensis. Folia Oeconomica
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2004
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vol. 177
EN
In this paper option pricing is treated as an application of Bayesian predictive analysis. The distribution of the discounted payoff, induced by the predictive density of future observables, is the basis for direct option pricing, as in Bauwens and Lubrano (1997). We also consider another, more eclectic approach to option pricing, where the predictive distribution of the Black-Scholes value is used (with volatility measured by the conditional standard deviation at time of maturity). We use a model framework that allows for two types of asymmetry in GARCH processes: skewed t conditional densities and different reactions of conditional scale to positive/negative stocks. Our skewed t-GARCH(l, 1) model is used to describe daily changes of the Warsaw Stock Exchange Index (WIG) from 4.01.1995 till 8.02.2002. The data till 28.09.2001 are used to obtain the posterior and predictive distributions, and to illustrate Bayesian option pricing for the remaining period.
PL
W prezentowanym artykule wycena opcji jest traktowana jako jedno z zastosowań bayesowskiej analizy predyktywnej. Rozkład wartości zdyskontowanej wypłaty, indukowany przez gęstość predyktywną przyszłych stóp zwrotu, jest podstawą bezpośredniej wyceny opcji (zob. Bauwens, Lubrano, 1997). Rozważamy też bardziej eklektyczne podejście, wykorzystujące rozkład predyktywny formuły Blacka i Scholesa (ze zmiennością określoną jako warunkowe odchylenie standardowe w momencie realizacji opcji). Przyjmujemy ramy modelowe, które uwzględniają dwa rodzaje asymetrii w procesach GARCH: skośne rozkłady warunkowe (typu t-Studenta) oraz zróżnicowane reakcje wariancji warunkowej na szoki dodatnie lub ujemne. Model: skośny £-GARCH(l, 1) jest stosowany do opisu dziennej zmienności Warszawskiego Indeksu Giełdowego (WIG) od 4.01.1995 r. do 8.02.2002 r. Dane do 28.09.2001 wykorzystujemy do budowy rozkładów a posteriori i predyktywnego oraz do ilustracji bayesowskiej wyceny opcji na pozostały okres.
2
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Forecasting currency covariances using machine learning tree-based algorithms with low and high prices

100%
Bejger S., Fiszeder P.
Przegląd Statystyczny
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2021
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vol. 68
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issue 3
1-15
EN
We combine machine learning tree-based algorithms with the usage of low and high prices and suggest a new approach to forecasting currency covariances. We apply three algorithms: Random Forest Regression, Gradient Boosting Regression Trees and Extreme Gradient Boosting with a tree learner. We conduct an empirical evaluation of this procedure on the three most heavily traded currency pairs in the Forex market: EUR/USD, USD/JPY and GBP/USD. The forecasts of covariances formulated on the three applied algorithms are predominantly more accurate than the Dynamic Conditional Correlation model based on closing prices. The results of the analyses indicate that the GBRT algorithm is the bestperforming method.
3
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Forecasting volatility during the outbreak of Russian invasion of Ukraine: application to commodities, stock indices, currencies, and cryptocurrencies

100%
Fiszeder P., Małecka M.
Equilibrium. Quarterly Journal of Economics and Economic Policy
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2022
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vol. 17
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issue 4
939-967
EN
Research background: The Russian invasion on Ukraine of February 24, 2022 sharply raised the volatility in commodity and financial markets. This had the adverse effect on the accuracy of volatility forecasts. The scale of negative effects of war was, however, market-specific and some markets exhibited a strong tendency to return to usual levels in a short time. Purpose of the article: We study the volatility shocks caused by the war. Our focus is on the markets highly exposed to the effects of this conflict: the stock, currency, cryptocurrency, gold, wheat and crude oil markets. We evaluate the forecasting accuracy of volatility models during the first stage of the war and compare the scale of forecast deterioration among the examined markets. Our long-term purpose is to analyze the methods that have the potential to mitigate the effect of forecast deterioration under such circumstances. We concentrate on the methods designed to deal with outliers and periods of extreme volatility, but, so far, have not been investigated empirically under the conditions of war. Methods: We use the robust methods of estimation and a modified Range-GARCH model which is based on opening, low, high and closing prices. We compare them with the standard maximum likelihood method of the classic GARCH model. Moreover, we employ the MCS (Model Confidence Set) procedure to create the set of superior models. Findings & value added: Analyzing the market specificity, we identify both some common patterns and substantial differences among the markets, which is the first comparison of this type relating to the ongoing conflict. In particular, we discover the individual nature of the cryptocurrency markets, where the reaction to the outbreak of the war was very limited and the accuracy of forecasts remained at the similar level before and after the beginning of the war. Our long-term contribution are the findings about suitability of methods that have the potential to handle the extreme volatility but have not been examined empirically under the conditions of war. We reveal that the Range-GARCH model compares favorably with the standard volatility models, even when the latter are evaluated in a robust way. It gives valuable implication for the future research connected with military conflicts, showing that in such period gains from using more market information outweigh the benefits of using robust estimators.
4
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The Polish contribution to financial econometrics. A review of methods and applications

86%
Osińska M.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2016
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issue 4 (54)
9-35
EN
Since 1982 the term “financial econometrics” has been present in the enormous literature that covers both methodologies and empirical analyses of the processes observed on the financial markets. The purpose of the presented paper is to indicate the milestones in financial econometrics and their usefulness and to show the contribution of the research from Poland into its development. ‘Pure’ financial econometrics methods are of special interest. The paper is directed at reviewing the recent methodologies and their applications. We focused on the contribution of Polish researchers into financial econometrics over the years, considering both the methodology and the applications. Some of the indicated publications are cited quite often, including international quotations, others are not very popular due to the language of the publication or the local reach of the journal, although many of them can be considered in line with the achievements that are presented in international empirical publications.
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