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...