dc.description.abstract | Although it is relatively difficult to predict the exact return associated with a stock, one can
compute, with a certain degree of precision, the volatility associated with the stock’s return by
utilizing appropriate mathematical models. In order to account for volatility, a new metric called the
Volatility Index (VIX), based on S&P 100 shares, was posited by the Chicago Board Options Exchange
(CBOE). This definition was tweaked eventually to make S&P 500 shares (SPX) the basis for
calculating VIX by averaging the prices of calls and puts on SPX shares (over a wide range of strike
prices) considering a time frame of 30 days. Futures and options eventually emerged based on the
VIX and have gone on to acquire a very critical role in financial markets worldwide, especially after
the Global Recession. Thus, quite intuitively, one can infer that it is possible to decode the dynamics
of SPX shares from the dynamics of the options based on them.
One of the interesting features of VIX (which computes a close approximation of the 30 day variance
swap rate) is that its computation is starkly different from the implied volatility derived from the
Black-Scholes model used by traders. The rationale behind using such a model is to account for the
“skew” effect occurring in stock prices which leads the Black-Scholes model to fail to account for
random volatility and thereby predict option prices which fall with an increase in the strike price of
the option. There have been two kinds of methods widely discussed in literature used for pricing VIX
options: model-free approaches and model-dependent approaches. In particular, the modeldependent approaches consider the underlying process to be stochastic in nature so as to arrive at a
feasible model for estimating VIX options prices wherein the model parameters are derived by
analyzing past data pertaining to these options. As quite evident, there does exist a disconnect in
approaches utilizing tweaked versions of the Black-Scholes model to price volatility options given
that the computation of the VIX (i.e. the most accurate volatility estimate) is primarily done on the
basis of the average bid-ask spread pertaining to these options. Secondly, the options and stocks are
priced based upon forward-looking data while the underlying assets are not thereby further
widening the afore-mentioned disconnect. Finally, very few models take bootstrapping of past
market data on a relatively dynamic scale into consideration while arriving at the model parameters,
whose validity may be established based on empirical studies. | en_US |