Volatility Library

Article by: Lyndon Lyons and Prof. Dr. Notger Carl
Published by: Würzburg-Schweinfurt University of Applied Sciences
Date: April 2005

“The volatility index, sometimes called by financial professionals and academics as
“the investor gauge of fear” has developed overtime to become one of the highlights
of modern day financial markets. Due to the many financial mishaps during the last
two decades such as LTCM (Long Term Capital Management), the Asian Crisis just
to name a few and also the discovery of the volatility skew, many financial experts
are seeing volatility risk as one of the prime and hidden risk factors on capital
markets. This paper will mainly emphasize on the developments in measuring and
estimating volatility with a concluding analysis of the historical time series of the new
volatility indices at the Deutsche Boerse.”

Full article (PDF): Link

Article by: Ahsan Amin
Published by: Infiniti Derivatives Technologies
Date: 13 Nov 2012

“In this paper, we solve the problem of solution of stochastic volatility models in which the volatility diffusion can be solved by a one dimensional Fokker-planck equation. We use one dimensional transition probabilities for the evolution of PDE of variance. We also find dynamics of evolution of expected value of any path dependent function of stochastic volatility variable along the PDE grid. Using this technique, we find the conditional expected values of moments of log of terminal asset price along every node of one dimensional forward Kolmogorov PDE. We use the conditional distribution of moments of above path integrals along the variance grid and use Edgeworth expansions to calculate the density of log of asset price. Main result of the paper gives dynamics of evolution of conditional expected value of a path dependent function of volatility (or any other SDE) at any node on the PDE grid using just one dimensional PDE if we can describe its one step conditional evolution between different nodes of the PDE.”

Full article (PDF): Link

Published by: FINCAD
Date: 2008

“Rather than gaining exposure to the market’s volatility through standard call and put options, investors can take views on the future realized volatility directly by trading derivatives on variance and volatility. The simplest such instruments are variance and volatility swaps.

“A volatility swap is a forward contract on future realized price volatility. Similarly, a variance swap is a forward contract on future realized price variance, variance being the square of volatility. At expiry the receiver of the “floating leg” pays (or owes) the difference between the realized variance (or volatility) and the agreed upon strike. At inception the strike is generally chosen such that the fair value of the swap is zero. This strike is referred to as fair variance (or fair volatility).”

Full article: Link

Article by: Anatoliy Swishchuk
Published by: Journal of Energy Markets
Date: 8 Jun 2011

“This paper focuses on the pricing of variance and volatility swaps in the energy market. An explicit variance swap formula and a closed-form volatility swap formula (using the Brockhaus–Long approximation) for energy assets with stochastic volatility are found. These formulas follow the continuous-time generalized autoregressive conditional heteroskedasticity(1,1).GARCH.1; 1//model (meanreverting) or the Pilipovi´c one-factor model. A numerical example is presented for the AECO natural gas index.”

Full article (PDF): Link
Presentation (PDF): Link