Risk Latte - The High and Low of Asset Prices - Parkinson's Approach

The High and Low of Asset Prices - Parkinson's Approach

Team Latte
August 8, 2006

Michael Parkinson, a physicist, in 1980 showed that the trading range of a security (stocks, currencies, etc.) contains significantly more information about the return generating process than the simple period to period return, i.e. market close-to-close. This was a seminal piece of work, though many professionals out the field of exotic options trading hardly know about it.

Parkinson's number attempts to estimate the volatility of returns for an asset following a diffusion process (geometric random walk) by using only the high and low of the period. Essentially, the simple formula, gives the distribution of the maxima and the minima of the asset returns. Parkinson's number P for an asset, say a stock or Treasury futures, is given by:

Comparing the Parkinson's number with the periodically sampled volatility can reveal very important information to traders, especially exotic option traders trading knock-outs or lookbacks, about the nature of mean reversion of the asset path as well as the distribution of stop losses. From the above formula it is obvious that the theoretical relationship between Parkinson's number and the periodically sampled volatility is:

Parkinson's Number (P) = 1.67 * Historical Volatility

If the Parkinson's number is more than 1.67 times the historical volatility (over the same continuous sample period) then the traders can infer that there is a clear bias in favour of a wider high-low range than is assumed by a random walk.

Given the high volatility environment today and a growing volume in the volatility products (variance swaps, vol swaps, short strangles, etc.) it would be interesting to see how the Parkinson's number compares with the historical volatility in various asset markets

(Reference : Efficient Estimation of Intraday Volatility: A Method-of-Moment Approach Incorporating Trading Range by Richard B Spurgin & Thomas Schneeweis (CISDM working paper) and Nassim Taleb's Dynamic Hedging .)

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