Volatility Library

Article by: Siân Williams
Published by: Futures and Options Intelligence
Date: 13 Dec 2010

“The Volatility Exchange (VolX) is considering launching contracts on the volatility of metals, rates and stock indices, its chief executive told FOi.

“The exchange has a patented methodology which calculates realised volatility over a specific time period. It uses closing prices of an asset over a defined period of one, three or twelve months to calculate the asset’s volatility over that period. It contrasts with the VIX methodology, which uses options to calculate implied volatility. Implied volatility is based on perceived volatility and realised volatility is actual volatility.

“The products are similar to volatility swaps and variance swaps, which are…”

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Article by: Peter Carr, Roger Lee, and Liuren Wu
Published by: NYU
Date: 6 Apr 2009

“We prove that a multiple of a log contract prices a variance swap, under arbitrary exponential Levy dynamics, stochastically time-changed by an arbitrary continuous clock having arbitrary correlation with the driving Levy process, subject to integrability conditions. We solve for the multiplier, which depends only on the Levy process, not on the clock. In the case of an arbitrary continuous underlying returns process, the multiplier is 2, which recovers the standard no-jump variance swap pricing formula as a special case of our framework. In the presence of negatively- skewed jump risk, however, we prove that the multiplier exceeds 2, which agrees with calibrations of time-changed Levy processes to equity options data. Finally we show that discrete sampling increases variance swap values, under an independence condition; so if the commonly-quoted 2 multiple undervalues the continuously-sampled variance, then it undervalues furthermore the discretely-sampled variance.”

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