Volatility Library

Article by: Peter Carr, Liuren Wu
Published by: Review of Financial Studies
Date: 2008

“We propose a direct and robust method for quantifying the variance risk premium on
financial assets. We show that the risk-neutral expected value of return variance, also
known as the variance swap rate, is well approximated by the value of a particular portfolio
of options.We propose to use the difference between the realized variance and this synthetic
variance swap rate to quantify the variance risk premium. Using a large options data set,
we synthesize variance swap rates and investigate the historical behavior of variance risk
premiums on five stock indexes and 35 individual stocks.”

Full article (PDF): Link

Article by: Peter Carr, Roger Lee
Published by: New York University
Date: 27 Aug 2009

“Volatility derivatives are a class of derivative securities where the payoff explicitly depends on some measure of the volatility of an underlying asset. Prominent examples of these derivatives include variance swaps and VIX futures and options. We provide an overview of the current market for these derivatives. We also survey the early literature on the subject. Finally, we provide relatively simple proofs of some fundamental results related to variance swaps and volatility swaps.”

Full article (PDF): Link