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EN
A large package of information is being reflected in stock prices during a short period after opening. Moreover, the start-of-the-day (morning) volatility has a strong impact on the price variability during all the day. In this connection, the question is whether the morning realized variance calculated as the sum of morning squared intraday returns can be useful in forecasting the daily realized variance (end-of-the-day volatility). In the paper, we apply three different methods of forecasting the daily realized variance for stocks quoted on the Warsaw Stock Exchange Our findings show that the morning realized variance provides valuable information that can be used in forecasting the daily realized variance.
EN
This paper is concerned with a dependence analysis of returns, return volatility and trading volume for five companies listed on the Vienna Stock Exchange. Taking into account the high frequency data for these companies, tests based on a comparison of Bernstein copula densities using the Hellinger distance were conducted. It is worth noting that these tests can be used in general settings since there is no restrietion on the dimension of the data. The parameter which must be set up for the testing procedure is a bandwidth. It is necessary for estimation of the nonparametric copula. The paper presents some patterns of causal relationships between stock returns, realized volatility and expected and unexpected trading volume. There is linear causality running from realized volatility to expected trading volume, and a lack of nonlinear dependence in the opposite direction. The authors detected strong linear and nonlinear causality from stock returns to expected trading volume. Therefore, a knowledge of past stock returns can improve forecasts of expected trading volume. They did not find causality running in the opposite direction.
EN
In this study, we analyse the performance of option pricing models using 5-minutes transactional data for the Japanese Nikkei 225 index options. We compare 6 different option pricing models: the Black (1976) model with different assumptions about the volatility process (realized volatility with and without smoothing, historical volatility and implied volatility), the stochastic volatility model of Heston (1993) and the GARCH(1,1) model. To assess the model performance, we use median absolute percentage error based on differences between theoretical and transactional options prices. We present our results with respect to 5 classes of option moneyness, 5 classes of option time to maturity and 2 option types (calls and puts). The Black model with implied volatility (BIV) comes as the best and the GARCH(1,1) as the worst one. For both call and put options, we observe the clear relation between average pricing errors and option moneyness: high error values for deep OTM options and the best fit for deep ITM options. Pricing errors also depend on time to maturity, although this relationship depend on option moneyness. For low value options (deep OTM and OTM), we obtained lower errors for longer maturities. On the other hand, for high value options (ITM and deep ITM) pricing errors are lower for short times to maturity. We obtained similar average pricing errors for call and put options. Moreover, we do not see any advantage of much complex and time-consuming models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare the results we obtain here with a detailed study for Polish emerging option market (Kokoszczyński et al. 2010b).
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