Volatility Library

Article by: Kenneth R. French, G. William Schwet, Robert F. Stambaugh
Published by: Journal of Financial Economics
Date: Dec 1986

“This paper examines the relation between stock returns and stock market volatility. We find
evidence that the expected market risk premium (the expected return on a stock portfolio minus
the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is
also evidence that unexpected stock market returns are negatively related to the unexpected
change in the volatility of stock returns. This negative relation provides indirect evidence of a
positive relation between expected risk premiums and volatility.”

Full article (PDF): Link

Article by: Peter Carr and Dilip Madan
Published by: NYU
Date: 30 Jan 2002

“The primary purpose of this article is to review three methods which have emerged for trading realized
volatility. The first method reviewed involves taking static positions in options. The classic example is
that of a long position in a straddle, since the value usually increases with a rise in volatility. The second
method reviewed involves delta-hedging an option position. If the investor is successful in hedging away
the price risk, then a prime determinant of the profit or loss from this strategy is the difference between the realized volatility and the anticipated volatility used in pricing and hedging the option. The final method reviewed for trading realized volatility involves buying or selling an over-the-counter contract whose payoff is an explicit function of volatility. The simplest example of such a volatility contract is a vol swap. This contract pays the buyer the difference betweeen the realized volatility3 and the fixed swap rate determined at the outset of the contract.”

Full article (PDF): Link

Article by: Peter Carr and Roger Lee
Published by: University of Chicago
Date: 31 May 2009

“In a nonparametric setting, we develop trading strategies to replicate volatility derivatives
— contracts which pay functions of the realized variance of an underlying asset’s returns. The
replicating portfolios trade the underlying asset and vanilla options, in quantities that we express in terms of vanilla option prices, not in terms of parameters of any particular model. Likewise, we find nonparametric formulas to price volatility derivatives, including volatility swaps and variance options. Our results are exactly valid, if volatility satisfies an independence condition. In case that condition does not hold, our formulas are moreover immunized, to first order, against nonzero correlation.”

Full article (PDF): Link