Volatility Library

Article by: Peter Larkin
Published by: Kellogg College, University of Oxford
Date: 18 Apr 2012

“Over the last years, there has been a growing interest in pricing and hedging financial products contingent on the volatility or variance of tradable assets. In parallel to this, there is a fundamental need to price in such a way as to capture all the information available in the market – in particular, in the observed implied volatility smile.

“The volatility of an equity is the simplest measure of how risky it is, or perhaps how much it is likely to move around in the future, based on how it has moved historically, or what the market implies it to be in the future. Investors may wish to trade volatility if they believe they have some insight into the level of future volatility. For example, if a trader thinks that volatility is currently too low, he or she may want to take a position which allows them to profit if volatility increases.

“In this work we are interested in a one important part of this growing area – the pricing and hedging or European options whose pay-off at maturity depends on the quadratic variation of the underlying process.”

Full article (PDF): Link

Article by: Asli Oztukel
Published by: Mathematical Institute, Oxford
Date: 1999

“In this paper we build upon the recently developed uncertain parameter framework for valuing derivatives in a worst-case scenario. We start by deriving a stochastic volatility model based on a simple analysis of time-series data. We use this stochastic model to examine the time evolution of volatility from an initial known value to a steady-state distribution in the long run. This empirical model is then incorporated into the uncertain parameter option valuation framework to provide ‘confidence limits’ for the option value.”

Full article (PDF): Link

Article by: Andrew J. Patton, Kevin Sheppard
Published by: Duke University
Date: 7 Oct 2011

“Using recently proposed estimators of the variation of positive and negative returns (“realized semivariances”), and high frequency data for the S&P 500 index and 105 individual stocks, this paper sheds new light on the predictability of equity price volatility. We show that future volatility is much more strongly related to the volatility of past negative returns than to that of positive returns, and this effect is stronger than that implied by standard asymmetric GARCH models. We also find that the impact of a jump on future volatility critically depends on the sign of the jump, with negative (positive) jumps in prices leading to significantly higher (lower) future volatility. A simple model exploiting these findings leads to significantly better out-of-sample forecast performance, across forecast horizons ranging from 1 day to 3 months”

Full article (PDF): Link