Working Papers contain preliminary research results. Please consider this when citing the paper. Please contact the authors to give comments or to obtain revised version. Any mistakes and the views expressed herein are solely those of the authors M Mo om me en nt tu um m a an nd d c co on nt tr ra ar ri ia an n e ef ff fe ec ct ts s o on n t th he e c cr ry yp pt to oc cu ur rr re en nc cy y m ma ar rk ke et t K Kr rz zy ys sz zt to of f K Ko oś ść ć* *, , P Pa aw we eł ł S Sa ak ko ow ws sk ki i, , R Ro ob be er rt t Ś Śl le ep pa ac cz zu uk k

This paper compares option pricing models, based on Black model notion (Black, 1976), especially focusing on the volatility models implied in the process of pricing. We calculated the Black model with historical (BHV), implied (BIV) and several different types of realized (BRV) volatility (additionally searching for the optimal interval Δ, and parameter n -the memory of the process). Our main intention was to find the best model, i.e. which predicts the actual market price with minimum error. We focused on the HF data and bidask quotes (instead of transactional data) in order to omit the problem of non-synchronous trading and additionally to increase the significance of our research through numerous observations. After calculation of several error statistics (RMSE, HMAE and HRMSE) and additionally the percent of price overpredictions, the results confirmed our initial intuition that that BIV is the best model, BHV being the second best, and BRV -the least efficient of them. The division of our database into different classes of moneyness ratio and TTM enabled us to observe the distinct differences between compared pricing models. Additionally, focusing on the same pricing model with different volatility processes results in the conclusion that point-estimate, not averaged process of RV is the main reason of high errors and instability of valuation in high volatility environment. Finally, we have been able to detect "spurious outliers" and explain their effect and the reason for them owing to the multi-dimensional comparison of the pricing error statistics.

In this paper we analyze class size effects in the case of primary schools in Poland. We use two empirical strategies to avoid endogeneity bias. First, we use average class size in a grade as an instrumental variable for actual class size. This allows us to control for within school selection of pupils with different abilities to classes of different sizes. Additionally, we estimate fixed effects for schools to control for differences between them. Second, we exploit the fact that there is an informal maximum class size rule. We estimate class size effect only for those enrollment levels where some schools decide to add a new class and thus dramatically lower class sizes. For such enrollment levels variance of class size is mainly exogenous and we argue that this allows to estimate quasi-experimental class size effects. In this case we again use average class size as an instrument with enrollment as a key control variable. Using both strategies we obtain similar findings. We found that the positive effects observed with OLS regression disappear when we use instrumental variables. If we avoid endogeneity bias, then class size negatively affects student achievement. However, this effect is rather small. We discuss methodology, possible bias of results and the importance of our findings to current policy issues in Poland.JEL: I2, H52, C31

Cholecystectomy is the surgical removal of the gallbladder. It is the most common method for treating symptomatic gallstones. Despite the existence of well-established treatment guidelines, the rate of cholecystectomy varies widely across Europe. We analyse patients in 10 countries that had undergone surgery for the treatment of symptomatic gallstones. We test the performance of three models in explaining variation in the (log of) cost of the inpatient stay (seven countries) or length of stay (three countries). The first model includes only the diagnosis-related group (DRG) variables to which cholecystectomy patients were coded (M D ), the second uses a core set of patient characteristics and episode-specific explanatory variables (M P ), and finally, the third model combines both sets of variables (M F ). Countries vary both in the number of DRGs used to classify cholecystectomy patients (range: 2-8), and in the percentage of patients covered by a single DRG (range: 50%-92%). The ability of combining both DRGs and patient level variables to explain cost variation among patients ranges from 58% in Spain to over 81% in Finland. The comparison of models' performance suggests that incorporating relevant patient characteristics may significantly improve DRG systems.