Implied volatility measures

In this thesis the construction of implied volatility measures is considered. Two popular option pricing models, namely Black-Scholes model and Cox-Ross-Rubinstein binomial model, are derived, solved and their inversion is considered to obtain implied volatility estimates. In addition, current market volatility indexes used by practitioners are discussed and Chicago Board Options Exchange's (CBOE) VIX index is derived in detail. Implied volatility measures rely heavily on the underlying assumptions of the option pricing models. In this thesis we assume the underlying asset to follow the geometric Brownian motion. The geometric Brownian motion is derived and the implications of the motion are discussed. Also, other assumptions in the pricing models are discussed. Due to some unrealistic assumptions in the pricing models, implied volatility measures have limitations and problems. These problems are introduced and the ways to alleviate these problems are discussed