# Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model

*Fred Espen Benth*,
*Martin Groth* and
*Rodwell Kufakunesu*

*Applied Mathematical Finance*, 2007, vol. 14, issue 4, pages 347-363

**Abstract:**
Following the increasing awareness of the risk from volatility fluctuations, the market for hedging contracts written on realized volatility has surged. Companies looking for means to secure against unexpected accumulation of market activity can find over-the-counter products written on volatility indices. Since the Black and Scholes model require a constant volatility the need to consider other models is obvious. Swaps written on powers of realized volatility in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard are investigated. A key formula is derived for the realized variance able to represent the swap price dynamics in terms of Laplace transforms, which makes fast numerical inversion methods viable. An example using the fast Fourier transform is shown and compared with the approximation proposed by Brockhaus and Long.

**Keywords:** Risk; hedging contracts; realized volatility; stochastic volatility; Levy processes; Laplace transforms (search for similar items in EconPapers)

**Date:** 2007

**References:** Add references at CitEc

**Citations** View citations in EconPapers (5) Track citations by RSS feed

**Downloads:** (external link)

http://www.tandfonline.com/doi/abs/10.1080/13504860601170609 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** http://EconPapers.repec.org/RePEc:taf:apmtfi:v:14:y:2007:i:4:p:347-363

**Ordering information:** This journal article can be ordered from

http://www.tandfonline.com/pricing/journal/RAMF20

Access Statistics for this article

Applied Mathematical Finance is currently edited by *Professor Ben Hambly* and *Christoph Reisinger*

More articles in Applied Mathematical Finance from Taylor & Francis Journals

Series data maintained by Michael McNulty ().