Implicit Volatilities (PDF)

Inhaltsangabe:Introduction:
Volatility is a crucial factor widely followed in the financial world. It is not only the single unknown determinant in the Black & Scholes model to derive a theoretical option price, but also the fact that portfolios can be diversified and hedged with volatility makes it a topic, which is crucial to understand for market participants comprising a wide group of private investors and professional traders as well as issuers of derivative products upon volatility.
The year 1973 was in several respects a crucial year for implicit volatility. The breakdown of the Bretton-Wood-System paved the way for derivative instruments, because of the beginning era of floating currencies. Furthermore Fischer Black and Myron Samuel Scholes published in 1973 the ground breaking Black & Scholes (BS) model in the Journal of Political Economy. This model was adopted in 1975 at the Chicago Board Options Exchange (CBOE), which also was founded in the year 1973, for pricing options. Especially since 1973 volatility has become a tremendously debated topic in financial literature with continually new insights in short-time periods.
Volatility is a central feature of option-pricing models and emerged per se as an independent asset class for investment purposes. The implicit volatility, the topic of the thesis, is a market indicator widely used by all option market practitioners.
In the thesis the focus lies on the implicit (implied) volatility (IV). It is the estimation of the volatility that perfectly explains the option price, given all other variables, including the price of the underlying asset in context of the BS model.
At the start the BS model, which is the theoretical basic of model-specific IV models, and its variations are discussed. In the concept of volatility IV is defined and the way it is computed is given as well as a look on historical volatility. Afterwards the implied volatility surface (IVS) is presented, which is a non-flat surface, a contradiction to the ideal BS assumptions. Furthermore, reasons of the change of the implied volatility function (IVF) and the term structure are discussed. The model specific IV model is then compared to other possible volatility forecast models. Then the model-free IV methodology is presented with a step-to-step example of the calculation of the widely followed CBOE Volatility Index VIX. Finally the VIX term structure and the relevance of the IV in practice are shown up. To ensure a good [...]