Oceňování evropských opcí

The main aim of this master thesis is to find a method that would provide an option valuation in accordance with market valuation. The principal model for the valuation of European options is the Black-Scholes model, which does not always produce correct results. The discrepancy between market prices and outcomes of Black-Scholes formula is usually explained by the issue of underlying asset volatility, but this investigation proves that the problem may be that the incorrect assumption about the process which is used for a description of underlying price development. In this study the European-style option, specifically S&P 500 option (SPX Weeklys), is analyzed using different models for the underlying price development (geometric Brownian motion as in case of Black-Scholes model, ARIMA, random walk etc.). The results illustrate that investors in the market do not use the Black-Scholes model for the valuation of European-style options but use presumption that the underlying asset price development follows random walk or potentially determined by empirical distribution.