Volatility Swaps and Volatility Options on Discretely Sampled Realized Variance

41 Pages Posted: 9 Sep 2013 Last revised: 23 Aug 2014

See all articles by Guanghua Lian

Guanghua Lian

University of South Australia - School of Commerce

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

Petko S. Kalev

La Trobe Business School

Date Written: August 9, 2014

Abstract

Volatility swaps and variance options are financial products written on discretely sampled realized variance. Actively traded in over-the-counter markets, these products are priced often by a continuously sampled approximation to simplify the computations. This paper presents an analytical approach to efficiently and accurately price discretely sampled volatility derivatives, under the Heston stochastic volatility model. We first obtain an accurate approximation for the characteristic function of the discretely sampled realized variance. This characteristic function is then applied to derive semi-analytical (up to an inverse Laplace transform) pricing formulae for variance options, volatility swaps and volatility options. We examine with numerical examples the accuracies of the approach in pricing these volatility derivatives. We also test the effect of discrete sampling in pricing volatility derivatives. For realistic contract specifications and model parameters, we find that although continuously sampled variance swaps and options are cheaper than their discretely sampled counterparts, continuously sampled volatility swaps are, however, more expensive than their discretely sampled counterparts.

Keywords: Variance swaps, Variance options, Stochastic volatility, Characteristic function

Suggested Citation

Lian, Guanghua and Chiarella, Carl and Kalev, Petko S., Volatility Swaps and Volatility Options on Discretely Sampled Realized Variance (August 9, 2014). Journal of Economic Dynamics and Control, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2322416 or http://dx.doi.org/10.2139/ssrn.2322416

Guanghua Lian (Contact Author)

University of South Australia - School of Commerce ( email )

37-44 North Terrace
Adelaide SA 5000, South Australia 5001
Australia

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Petko S. Kalev

La Trobe Business School ( email )

Department of Economics and Finance
Donald Whitehead Building: Level 3, DWB313
Bundoora, Victoria 3086
Australia
+613 9479 6285 (Phone)
+613 9479 1654 (Fax)

HOME PAGE: http://www.latrobe.edu.au/business/about/staff/profile?uname=PKalev

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