Implied Volatility is a concept rooted deep in financial derivatives pricing. Option pricing models, such as Black-Scholes, require an input of a volatility parameter of the underlying asset in order to arrive at an estimation of the option price. In B-S, this volatility is assumed to be constant.
Real world financial markets are far from constant in their volatility. It is therefore common to turn the question around: what volatility is needed for the option pricing model to arrive at the current, observed market price of the derivative? This is what's called an Implied Volatility (IV; implied by the current price). It can be calculated on an ongoing basis and be presented as a time series.
It is often assumed that Implied Volatility is a proxy measure of expected volatility to come, estimated from the current buyer/seller equilibrium. One such measure of Implied Volatility for US stocks is the VIX index, published and maintained by the CBOE. There exist similar indices for european stocks and selected commodities. However, not all markets have derivative instruments based on them, so it becomes impossible to estimate expected volatility in this regular way.
We compare the VIX index with the forward-looking realized volatility of the consecutive price changes of the underlying, and with a simple estimate based solely on past price activity. We find the correlation to be higher with the simple estimate.
Based on this observation, we propose a simpler estimator of IV - a Simulated Implied Volatility (SIV) index - constructed solely from historical price activity of the underlying instrument. This enables us to model the IV of assets with no derivatives set upon them. |