cahn's blog

 To start we need to go back to the Bible. In Genesis Chapter 29, believed to be about the year 1700 B.C., Jacob purchased an option costing him seven years of labor that granted him the right to marry Laban's daughter Rachel. His prospective father-in-law, however, reneged, perhaps making this not only the first derivative but the first default on a derivative.

In Variance Swap, the relationship between  Vega Notional (the dollar value per vega or volatility point) and Variance Notional (the dollar value per variance unit) is conventionally expressed as

The comes from the first order Taylor expansion (expand the function ).

The  Parkinson formula for estimating the historical volatility of an underlying based on high and low prices.

where

= Volatility
= Number of closing prices in a year
= Number of historical prices used in the volatility estimate
= The high
= The low

http://www.sitmo.com/eq/173

Yang and Zhang derived an extension to the Garman Glass historical volatility estimator that allows for opening jumps. It assumes Brownian motion with zero drift. This is currently the preferred version of open-high-low-close volatility estimator for zero drift and has an efficiency of 8 times the classic close-to-close estimator. Note that when the drift is nonzero, but instead relative large to the volatility, this estimator will tend to overestimate the volatility.

Original archived here. One tip, try using Macrium Reflect instead of DriveImage XML. The steps 2 to 13 will be much simpler and faster (see below).