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EN
The recent economic crisis of 2008/2009 boosted a discussion about effectiveness of popular methods of controlling risk in financial markets, with value-at-risk approach being a topical issue. The paper contrasted a GARCH model for 1% VaR estimation for WIG20 with five basic approaches: variance-covariance, historical simulation, Risk Metrics™, Monte Carlo simulation and bootstrap method. A comprehensive study was supplied, with the focus on sample choice, to emphasize the influence of extraordinary price movements during the crisis. The study showed that nonparametric methods prevail over other models in the sense that the probability of exceeding the assumed loss level is the lowest. Further enquiry supported the view that GARCH model outperforms all techniques based on the assumption of a specific probability distribution of log returns. The problem of attaining the required level of tolerance in conditions of high instability of prices was evident from Kupiec tests results. A complementary analysis of capital requirements in relation to VaR estimation technique, gave the additional argument for GARCH model superiority over other risk valuation methods.
PL
Kryzys przełomu lat 2008/2009 wywołał dyskusję dotyczącą efektywności popularnie stosowanych metod kontroli ryzyka na rynku finansowym, co w szczególności spowodowało wzrost zainteresowania metodologią VaR. W niniejszym opracowaniu przedstawione zostało porównanie metody VaR-GARCH do szacowania 1% VaR dla indeksu WIG20 z pięcioma innymi popularnymi podejściami: wariancji-kowariancji, symulacji historycznej, Risk Metrics™, Monte Carlo, metodą symulacyją i bootstrapową. Szczególną uwagę zwrócono na wybór próby, w celu podkreślenia wniosków specyficznych dla okresu kryzysu finansowego. Pokazano, że nieparametryczne metody przeważają nad pozostałymi w kontekście prawdopodobieństwa przekroczenia przewidywanego poziomu straty. Badanie potwierdziło hipotezę, że model GARCH daje lepsze rezultaty niż metody oparte na założeniu niezmiennego w czasie rozkładu logarytmicznych stóp zwrotu. Wyniki testu Kupca pokazały problem przekraczania założonego poziomu tolerancji w warunkach kryzysu. Badanie uzupełniono analizą wymogów kapitałowych w zależności od techniki estymacji VaR, co dodatkowo potwierdziło przewagę modelu GARCH nad innymi sposobami szacowania ryzyka.
PL
W pracy rozważany jest warunkowy model maksimów blokowych, wywodzący się z teorii wartości ekstremalnych. Badana jest jego przydatność do wyznaczania jednookresowych prognoz Value at Risk (VaR), gdy parametry modelu są szacowane na podstawie małej próby. Weryfikowana jest hipoteza, iż warunkowy model maksimów blokowych zwraca poprawne oszacowania VaR. Przeprowadzono empiryczną analizę poprawności modelu na siedmiu światowych indeksach giełdowych w latach 2001-2013. Badania potwierdziły, że model jest poprawny pod względem liczby i niezależności przekroczeń VaR oraz może być alternatywą dla innych często wykorzystywanych modeli.
EN
The model under consideration is conditional block maxima model. In this paper the usefulness of the model to determine one-ahead forecast VaR is taken into account, when the model parameters are estimated in small sample. The hypothesis, that conditional block maxima model is correct to estimate VaR forecasts is verified. We carried out an empirical analysis on seven world stock market indices in the years of 2001- 2013. The survey confirmed, that the model is correct in terms of number and independence of VaR exceedances and can be a good alternative to other often used models.
EN
The leverage effect is a situation in which volatility tends to increase dramat-ically following bad news, and to increase moderately (or even to diminish) following good news. An example of its occurrence is given. The universality of the leverage effect motivates the further part of the work in which asymmetric GARCH models are de-scribed. In particular, the EGARCH [Nelson, 1991], TGARCH [Zakoian, 1994], GJR- -GARCH [Glotsen, Jagannathan, Runkle, 1993] and APARCH [Ding, Granger, Engle, 1993] models are considered. Models are fit to the daily log-returns series of the Pioneer Akcji Polskich subfund. Parameter estimates are presented. Then a comparison of the considered models is carried out. The BIC criterion [Schwarz, 1978] is used as well as the means of the squared differences between the estimated volatilities.
PL
Efekt dźwigni jest to sytuacja, w której złe informacje powodują gwałtowny wzrost warunkowej zmienności, natomiast dobre informacje prowadzą jedynie do jej nieznacznego wzrostu lub nawet spadku. W opracowaniu podano przykład jego występowania. Powszechność efektu dźwigni motywuje dalszą część pracy, w której zostają opisane asymetryczne modele GARCH. W szczególności są to EGARCH [Nelson, 1991], TGARCH [Zakoian, 1994], GJR-GARCH [Glotsen, Jagannathan, Runkle, 1993] i APARCH [Ding, Granger, Engle, 1993]. Modele zostały dopasowane do dziennych zwrotów logarytmicznych subfunduszu Pioneer Akcji Polskich. W pracy przedstawiono estymowane parametry. Następnie przeprowadzono porównanie rozważanych modeli. Wykorzystano do tego kryterium BIC [Schwarz, 1978], jak również średniokwadratowe różnice pomiędzy estymowanymi warunkowymi zmiennościami.
PL
W pracy badamy kilka strategii odpornej estymacji parametrów modeli ARIMA i GARCH. Porównujemy między innymi podejścia wykorzystujące statystyczne funkcje głębi: wykorzy- stujące koncepcję głębi odnoszącą się do funkcji a zaproponowaną przez Lopez-Pintado i Romo (2005) oraz własne propozycje wykorzystujące głębie regresyjną.
EN
This paper determines whether the VaR estimation is influenced by conditional distribution of return rates (normal, t-student, GED) and attempts to choose the model which best estimates VaR on a selected example. We considered logarithmic return rates for the WIG-20 index from 1999-2011. Then, on their basis we estimates various types of ARIMA-GARCH (1,1) models. Applying relevant models we calculated VaR for the long and short position. The differences between the models were settled on the basis of the Kupiec test.
EN
It is generally acknowledged that squared daily returns on a financial instrument provide a poor approximation of its daily volatility. It was first pointed out by Andersen and Bollerslev that more accurate estimates are obtained with the realized volatility calculated as the sum of squared intraday returns corresponding to high-frequency data. In this paper we show how the volatility forecasts for the stock index WIG provided by the popular GARCH(I,I) improve when instead of daily squared returns they are evaluated against the realized volatility.
PL
Powszechnie uważa się, że kwadraty dziennych zwrotów instrumentu Finansowego słabo aproksymują jego dzienną zmienność. Andersen i Bollerslev jako pierwsi zauważyli, że bardziej dokładne oszacowania zmienności można otrzymać za pomocą zmienności liczonej jako suma kwadratów zwrotów śróddziennych, odpowiadających danym o wyższej częstotliwości. W niniejszym artykule pokazujemy, o ile poprawiają się prognozy zmienności indeksu giełdowego WIG, gdy zamiast do kwadratów zwrotów dziennych odnosi się je do zmienności zrealizowanej.
EN
The paper looks at seasonality effects displayed by share prices on the Warsaw Stock Exchange. The analysis covers four WSE indices and 30 selected companies. The author uses methods that make it possible to determine the “generalized autoregressive conditional heteroskedasticity” (GARCH) of financial instruments in terms of their rates of return. On the basis of his analysis, Grotowski concludes that, first of all, there is a visible “Thursday effect” as well as a “Friday effect” on the Polish stock market. On Thursdays and Fridays, the return on stock investments is generally higher than on other days of the week. Second, it is also possible to identify a “December effect” and a “January effect,” Grotowski says, though their importance varies from one market segment to another. Third, these calendar effects apply to a greater extent to the WSE’s indices rather than individual share prices. Fourth, from an economic point of view, the role of the calendar effects is limited and they are too insignificant to form the basis of a viable investment strategy.
EN
The notion of daily realized volatility introduced by Andersen and Bollerslev gave a new impulse to research connected with modeling and forecasting the volatility of financial returns using GARCH models. Daily realized volatility is a sum of squared intraday returns. Volatility forecasts obtained from GARCH models improve when instead of daily squared returns they are evaluated against the realized volatility. In this paper we calculate and investigate volatility forecasts for stock indices from the Warsaw Stock Exchange delivered by GARCH models with realized volatility as an additional explanatory variable.
PL
Wprowadzone przez Andersena i Boilersleva pojęcie dziennej zmienności zrealizowanej dało nowy impuls badaniom poświęconym modelowaniu i prognozowaniu zmienności cen instrumentów finansowych przy użyciu modeli GARCH. Dzienna zmienność zrealizowana jest określona jako suma kwadratów zwrotów śróddziennych. Odnoszenie dziennych prognoz modeli GARCH do tak rozumianej zmienności zwykle znacznie poprawia jakość prognozy. Praca poświęcona jest prognozowaniu dziennej zmienności zrealizowanej indeksów Warszawskiej Giełdy Papierów Wartościowych za pomocą modeli z rodziny GARCH, w których opóźniona dzienna zmienność zrealizowana została również wprowadzona jako dodatkowa zmienna objaśniająca.
EN
Research Background: The banking sector plays a crucial role in the world's economic development. This research paper evaluates the volatility spillover, symmetric, and asymmetric effects between the macroeconomic fundamentals, i.e., market risks, interest rates, exchange rates, and bank stock returns, for the listed banks of Pakistan. Purpose of the article: The main purpose of this study is to examine the volatility of Pakistani banking stock returns due to the influence of market risk, interest rates, and exchange rates. Pakistan is selected for the study because the volatility of its banking stock returns is strongly influential in achieving sustainable economic development. Methods: By applying the OLS with the Heteroskedasticity and Autocorrelation Consistent (HAC) covariance matrix, the GARCH (1, 2), and the EGARCH (1, 1), analysis is conducted for the period from January 1, 2009 to December 31, 2019 using samples of 13 listed banks. Findings & Value added: The ARCH parameter is significant in the OLS with the HAC covariance matrix estimation, which is a clear indication of the existence of heteroskedasticity in the squared residuals and the inaccuracy of the OLS with the HAC covariance matrix. The results of the OLS with the HAC covariance matrix suggest using the GARCH model family to accurately measure the volatility of bank stock prices. The results of the mean equation in the GARCH (1, 2) and EGARCH (1, 1) indicate the positive significance of market risk and the low significance of interest and exchange rates, confirming that market returns strongly affect the sensitivity of bank stock returns compared to interest and exchange rates. It should be noted that the ARCH (α) and GARCH (β) parameters of the variance equation fulfill the non-negative conditions of the GARCH model. Furthermore, the leverage parameter (λ) is found to be positively significant for all banks, and volatility is found to be influenced by positive shocks compared to negative shocks. Conclusively, it can be stated that market returns determine the dynamics of the conditional returns of bank stocks. Nevertheless, the interest and exchange rate volatilities determine the conditional bank stock returns' volatility.
EN
Under the impact of a wide range of forces, the prices of globally traded commodities often experience sudden and significant fluctuations, putting under uncertainty and risk the economic status of producers, consumers and traders from the private to the national level. Although commodity markets are notorious for their price volatility, the events the world economy experienced in recent years, particularly the global economic crisis, offered new connotations to this phenomenon. These price movements reverberated across internal markets all over the world, affecting their statuses. As Central Eastern European countries, due to the processes they have undergone in recent decades, manifest an increased responsiveness to external shocks, Romania experienced the international turmoil in a severe manner. This paper calculates and presents, by comparison, the food price volatility experienced at the international level and on the Romanian market during the years of the crisis and immediately after its appeasement.
PL
Celem artykułu jest porównanie oszacowań zmienności uzyskanych z modeli parametrycznych: GARCH i SV z oszacowaniem uzyskanym na podstawie zmienności zrealizowanej szacowanej w oparciu o dane różnej częstotliwości. W badaniu wzięto pod uwagę zwroty z wybranych instrumentów polskiego rynku finansowego: indeks WIG 20 oraz kurs walutowy EUR/PLN. Ujęta w badaniu próba objęła okres kryzysu finansowego, co stanowi istotne uzupełnienie wyników prezentowanych do tej pory w literaturze.
EN
The aim of the article is to compare the estimates of the volatility obtained from the parametric models: the GARCH and the SV with the estimates based upon the Realized Volatility approach, whereas the estimates from the RV are obtained from the data of different frequencies. The data sample consists of the WIG20 index and the EUR/PLN exchange rate and covers the hectic crisis period. Hence, the presented results can be viewed as an extension of the results of the studies presented up to date.
EN
Technique for American options valuation, combining Least Squares Monte Carlo with Duan\’s model under the assumption that the volatility of the underlier can be described by GARCH(1, 1) process, has been confronted with simple binomial tree model. Results of comparison of model outcomes with market prices for ten different CBOE-traded stock options indicate that simple binomial model is superior to sophisticated GARCH-LSM method. The results hold regardless of option characteristics—“moneyness” ratio and time to maturity. Incorporating dividend in binomial model does not significantly alter the valuation outcomes. Detailed analysis shows also that for each of the methods pricing errors grow as the “moneyness” ratio decreases.
PL
Celem niniejszego artykułu jest odpowiedź na pytanie, czy możliwe jest skuteczne prognozowanie wartości ryzyka rynkowego w warunkach polskiego rynku kapitałowego. Do analizy tego zagadnienia wykorzystano szeregi dziennych stóp zwrotu spółek notowanych na Giełdzie Papierów Wartościowych w Warszawie w latach 2000-2015. W części badawczej pracy przyjęto założenie, iż analizowane szeregi czasowe są realizacją procesu GARCH, co pozwoliło na modelowanie charakterystycznych właściwości spotykanych w empirycznych szeregach czasowych stóp zwrotu akcji giełdowych. Pomiaru ryzyka dokonano posługując się popularnymi miarami zagrożenia. Została również podjęta próba wyboru optymalnej spośród najpopularniejszych metod estymacji ryzyka.
EN
The aim of this paper is to investigate whether it is possible to successfully forecast market risk in the Polish capital market. To answer this question, daily time series of the stock prices listed on the Warsaw Stock Exchange between 2000-2015 are analysed. In the research part of the paper, it is assumed that the analysed time series are the realisation of the GARCH process, which allows the author to model the characteristic properties among the empirical data. The risk is assessed with the use of popular quantile risk measures. Additionally, an attempt is made to establish the optimal method of risk estimation.
EN
Research background: The Brexit referendum had a profound effect on the economic relations between the United Kingdom (UK) and continental Europe. Major economic and financial determinants were affected, including the impact of the GBP/EUR exchange rate volatility on the dynamics of UK exports to the Eurozone. Purpose of the article: This paper seeks to assess the extent to which these dynamics have changed since Brexit and to estimate the magnitude of their impact. Methods: To this end, the volatility behavior of the GBP/EUR exchange rate before and after Brexit is captured using EWMA, GARCH(p,q), and EGARCH(p,q) models for the period of January 1, 2010 to August 31, 2020. The post-Brexit change in the volatility structure of GBP/EUR exchange rates is then tested by including a dummy in the optimal volatility model. Finally, the Autoregressive Distributed Lag (ARDL) Bounds Testing approach is employed to analyze the relationships between exchange rate volatility and exports. Findings & value added: GARCH(1,1) was selected as the winning model and used to examine the volatility structure of the post-Brexit exchange rate, which revealed no significant change. By incorporating a well-grounded proxy for exchange rate volatility into the demand function of exports, and controlling for the industrial production index, terms of trade, and real exchange rate, the analysis showed that exchange rate volatility had a negative impact on export volume to the Eurozone in both the long and short run. Additionally, the industrial production index had a positive effect on export volume in both the long and short run, while an appreciation in the value of the pound relative to the euro adversely affected the competitiveness of UK exports in the Eurozone market in the long run, with no impact in the short run. This paper serves as a benchmark for future studies, as it follows a three-step modeling approach and provides valuable insights into the potential economic and financial consequences a European Union (EU) member state may face should it choose to exit the EU.
EN
This paper examines the impact of real exchange rate volatility on economic growth in Kenyan. The study employed the Generalized Autoregressive Condition of Heteroscedasticity (GARCH) and computation of the unconditional standard deviation of the changes to measure volatility and Generalized Method Moments (GMM) to assess the impact of the real exchange rate volatility on economic growth for the period January 1993 to December 2009. Data for the study was collected from Kenya National Bureau of Statistics, Central Bank of Kenya and International Monetary Fund Data Base by taking monthly frequency. The study found that RER was very volatility for the entire study period. Kenya’s RER generally exhibited a appreciating and volatility trend, implying that in general, the country’s international competitiveness deteriorated over the study period. The RER Volatility reflected a negative impact on economic growth of Kenya.
EN
Aim/purpose – This paper examines the relationship between exchange rate volatility and industrial output growth in Nigeria. In spite of the massive revenue emanating from oil wealth, Nigeria has wallowed in intergenerational poverty due to the inability to grow its industrial sector. The dilemma of exchange rate allowed growth of the industrial sector to become enormous. As such, this paper attempts a quantitative analysis of industrial output growth in Nigeria as predicted by an exchange rate volatility using a time series data from the exchange rate and the industry value added from 1986 through 2017. Design/methodology/approach – This paper adopts a quantitative analysis of exchange rate volatility as a predictor of changes in industrial output in Nigeria. Monthly Data on exchange rate from 1986 through 2017 were first analysed to show for their clustering behaviour. Thus, ascertaining whether they are volatile or not. The study employs AR(k)-EGARCH(p,q) models for the calculation of volatility in the growth rate of nominal exchange rates. Then the paper adopts the Auto-Regressive Distributed Lag Approach to account for the long-run and short-run dynamics of industrial output in Nigeria as induced by volatility in the exchange rate for different regimes under the scope. Findings – The findings reveal that the real exchange rate volatility determines industrial production as well as availability of foreign exchange increments arising from the various export drives contributing tremendously to the increase in the industrial output in Nigeria. It is further revealed that the capacity utilisation ratio was low. Research implications/limitations – Established evidence of low capacity utilisation may be due to the epileptic power supply, inadequate technological know-how. As such, the government should maintain a flexible exchange rate system to maximally harness the benefits of growth emanating from the industrial sector. Originality/value/contribution – The paper specifically offers an experimental proof to the underlying relationship between industrial output and exchange rate volatility in Nigeria. Previous studies reviewed in the literature have mostly focused on the growth effect of the exchange rate neglecting the important nexus it shares with the industrial sector (a bedrock of sustainable development).
EN
This article analyzes the impact of the capital market on economic growth in the US with the use of annual data. The study covers the years 1975-2019. As part of the analysis, the construction and estimation of an econometric model was made using the GRETL program. The obtained results confirmed the statistically significant influence of the capital market on the economic growth in the USA.
EN
In the study, the two-step EWS-GARCH models to forecast Value-at-Risk is presented. The EWS-GARCH allows different distributions of returns or Value-at-Risk forecasting models to be used in Value-at-Risk forecasting depending on a forecasted state of the financial time series. In the study EWS-GARCH with GARCH(1,1) and GARCH(1,1), with the amendment to the empirical distribution of random errors as a Value-at-Risk model in a state of tranquillity and empirical tail, exponential or Pareto distributions used to forecast Value-at-Risk in a state of turbulence were considered. The evaluation of Value-at-Risk forecasts was based on the Value-at-Risk forecasts and the analysis of loss functions. Obtained results indicate that EWS-GARCH models may improve the quality of Value-at-Risk forecasts generated using the benchmark models. However, the choice of best assumptions for the EWS-GARCH model should depend on the goals of the Value-at-Risk forecasting model. The final selection may depend on an expected level of adequacy, conservatism and costs of the model.
EN
Research background: Empirical market microstructure research has recently shifted its focus from the examination of liquidity of individual securities towards analyses of the common determinants and components of liquidity. The identification of commonality in liquidity emerged as a new and fast growing strand of the literature on liquidity. However, the results around the world are ambiguous and rather depend on a specific stock market. Purpose of the article: The aim of this study is to explore intra-market commonality in liquidity on the Warsaw Stock Exchange (WSE) by using daily proxies of six liquidity estimates: percentage relative spread, percentage realized spread, percentage price impact, percentage order ratio, modified turnover, and modified version of the Amihud measure. The sample covers a period from January 2005 to December 2016. The database contains the group of eighty-six WSE-listed companies. Methods: The research hypothesis that there is commonality in liquidity on the Polish stock market is tested. The OLS with the HAC covariance matrix estimation and the GARCH-type models are employed to infer the patterns of liquidity co-movements on the WSE. Moreover, because the sample period is quite long, the stability of the empirical results by time period is examined. Seven 6-year time windows are utilized in the study. Findings & Value added: The regression results reveal weak evidence of co-movements in liquidity on the WSE, regardless of the choice of the liquidity proxy. Furthermore, the robustness tests based on the time rolling-window approach do not unambiguously support the research hypothesis that there is commonality in liquidity on the Polish stock market. To the best of the author?s knowledge, the empirical findings presented here are novel and have not been reported in the literature thus far.
EN
Research background: The study analyzes whether financial speculation destabilizes commodity prices in light of recent price volatility and spikes in agricultural commodities. The study delves deeper into the US dairy futures markets, which are less studied by other authors in their research and relatively new in comparison to other agricultural commodity markets. These dairy commodity futures contracts provide dairy businesses and farmers the chance to hedge against price risks, which are particularly crucial in uncertain economic times such as the post-2020 COVID-19 pandemic timeframe. The analysis makes use of the weekly returns on futures contracts for nonfat milk powder, butter, milk class III, and cheese that are obtained from the Chicago Mercantile Exchange (CME). Purpose of the article: Conduct an empirical study to evaluate the effect of financial speculation on dairy product prices on US commodity markets, including the post-2020 timeframe. Methods: Time series analysis is used in the investigation: the generalized auto-regressive conditional heteroskedasticity (GARCH) method, the Granger causality test, and the Augmented Dickey-Fuller (ADF) test. Findings & value added: Our analysis's findings show that, even though most commodities experienced an increase in return volatility during the post-2020 period, there is no evidence for financial speculation being the cause of increased returns from dairy futures contracts. The research also suggests that financial speculation, in some cases, even lowers the volatility of dairy futures prices. Therefore, non-commercial market participants may help to distribute price risks, making these markets more liquid.
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