This paper compares option pricing models, based on the Black model (Black, 1976), with particular emphasis on volatility measures and estimators applied in the process of valuation. We calculate the Black model with historical (BHV), implied (BIV) and several different types of realized (BRV)...

Option pricing models are the main subject of many research papers prepared both in academia and financial industry. We check the properties of option pricing models with different assumptions concerning the volatility process (historical, realized, implied, stochastic or GARCH model). For this...

This paper investigates the changes in the investment portfolio performance after including VIX. We apply different models for optimal portfolio selection (Markowitz and Black-Litterman) assuming both the possibility of short sale and the lack of it. We also use various assets, data frequencies,...

We suggest that the term structure of volatility futures (e.g. VIX futures) shows a clear pattern of dependence on the current level of VIX index. At the low level of VIX (below 20) the term structure is highly upward sloping; at the high VIX level (over 30) it is strongly downward sloping. We...

This paper focuses on volatility of financial markets, which is one of the most important issues in finance, especially with regard to modeling high-frequency data. Risk management, asset pricing and option valuation techniques are the areas where the concept of volatility estimators...

This article aims to extend evaluation of the classic multifactor model of Carhart (1997) for the case of global equity indices and to expand analysis performed in Sakowski et. al. (2015). Our intention is to test several modifications of these models to take into account different dynamics of...

Introduction -- Volatility and its estimation -- Overview of volatility derivatives -- Options delta hedging with no options at all -- Volatility derivatives in portfolio optimization -- Benefits of using volatility futures in investment strategies -- Predictive properties of the volatility term...