Paweł Strawiński

Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures

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.

Changes in Return to Higher Education in Poland 1998-2005

In the article private rate of return to higher education in the 1998-2005 period is considered. The model is based on a comparative advantage theory. Extended Mincerian wage equation is used to account for a non-random decision to undertake studies at university level. The estimate of private rate of return in Poland is roughly 9%, and it is among the highest in Europe. In addition, the unexpected rise in rate of return is observed. Moreover, positive relationship between graduation and the obtained wages was found. This change has been linked to labour market transformation and Skill Biased Technical Change. Also the influence of financing tertiary education is considered.

External Return to Education in Poland

In the article social rate of return to education is considered. As is pointed out in various research papers social return rate exceeds the pure technical rate of return by considerable margin. However, it is hard to calculate adequate figure due to methodological and data problems. The model used in the article is based on a comparative advantage theory. It contains two equations: one for technical and social rate of return to education, second deals with non-random selection for different education regimes. We find that private rate of return is over 7% yearly and therefore is still among the highest in Europe and there exists additional 1.5% social return to higher education.

Analysis of HF Data on the WSE in the Context of EMH

This paper focuses on one of the heavily tested issue in the contemporary finance, i.e. efficient market hypothesis (EMH). However, we try to find the answers to some fundamental questions basing on the analysis of high frequency (HF) data from the Warsaw Stock Exchange (WSE). We estimate model on daily and 5-minute data for WIG20 index futures trying to verify daily and hourly effects. After implementing the base methodology for such testing, additionally we take into account the results of regression with weights, i.e. robust regression is used that assigns the higher weight the better behaved observations. Our results indicate that we observe the day of the week effect and hour of the day effect in polish data. What is more important is the existence of strong open jump effect for all days except Wednesday and positive day effect for Monday. Considering the hour of the day effect we observe positive, persistent and significant open jump effect and the end of session effect. Aforementioned results confirm our initial hypothesis that Polish stock market is not efficient in the information sense.