||Quantitative methods in finance are mainly based on an unrealistic assumption of normally distributed asset prices. In our research we follow two theoretical approaches that give out the unrealistic normality assumption and try to describe the "non-normal" behavior of asset prices. The first approach replaces normal distribution with an alternative and stronger distribution, able to capture empirically observed heavy-tailed, skewed asset prices or discontinuity in prices. The second approach relaxes the assumption of constant volatility and focuses on a dynamic behavior of asset prices distribution. Our research aims at examining possible utilization of modern asset prices models, mainly impacts of changes in assumptions into derivatives pricing (these include e.g. stochastic volatility models, jump models or usage of alternative, nonparametric methods such as neural networks) and risk management.