Comparison of the behaviour of market option prices in relation to option prices resulting from the black-scholes model during periods of a bull and bear market

In continuation to one of my previous papers (Kształtowanie się cen opcji indeksowych a ich wycena na podstawie modelu Blacka-Scholesa), where the research problem to what extent pricing of option using theoretical models is tangent to the behaviour of market option prices in Polish conditions was scrutinized, in the present work it is verified whether there exist significant differences between the behaviour of market option prices in relation to option prices resulting from the Black-Scholes model during periods of a bull and bear market. In order to make those comparisons, the parameters of the lines of regression describing the dependence of market prices of options for index WIG20 on their prices resulting from B-S model were calculated. On the basis of these calculations, it is possible to say how market prices resemble prices resulting from the model. The research was conducted for two periods of similar length, assuming that between 20 September 2004 and 18 March 2005 we had a bull market and during the days between 1 August 2008 and 20 March 2009 the market was bearish.