Volatility Library

Article by: Mark Broadie, Ashish Jain
Published by: Columbia Business School
Date: 10 Jan 2008

“This paper studies the pricing and hedging of variance swaps and other volatility derivatives, including volatility swaps and variance options, in the Heston stochastic volatility model. Pricing and hedging results are derived using partial differential equation techniques. We formulate an optimization problem to determine the number of options required to best hedge a variance swap. We propose a method to dynamically hedge volatility derivatives using variance swaps and a finite number of European call and put options.”

Full article (PDF): Link

Article by: Anatoliy Swishchuk
Published by: Department of Mathematics & Statistics, York University

“A new probabilistic approach is proposed to study variance and volatility swaps for financial markets with underlying asset and variance that follow the Heston (1993) model. We also study covariance and correlation swaps for the financial markets. As an application, we provide a numerical example using S&P60 Canada Index to price swap on the volatility.”

Full article (PDF): Link

Published by: FINCAD
Date: 2008

“The classic derivatives that allow investors to take a view on volatility are straddles or strangles. A long position in a straddle, for example, will generate a profit if the underlying asset price moves up or down, or if the implied volatility rises. However, these options are also sensitive to the underlying asset price, as the delta of a straddle or a strangle is zero only when the option is at-the-money.

Unlike these options, variance and volatility swaps provide pure exposure to volatility. A volatility swap is essentially a forward contract on future realized price volatility. At expiry the holder of a long position in a volatility swap receives (or owes if negative) the difference between the realized volatility and the initially chosen volatility strike, multiplied by a notional principal amount. A variance swap is analogously a forward contract on future realized price variance, which is the square of future realized volatility.

In both cases, at inception of the swap the strike is chosen such that the fair value of the swap is zero. This strike is then referred to as fair volatility and fair variance, respectively.”

Full article: Link