Derivatives on Volatility: Some Simple Solutions Based on Observables

Federal Reserve Bank of Atlanta WP No. 2000-20, November 2000

21 Pages Posted: 7 Nov 2000

See all articles by Steven L. Heston

Steven L. Heston

University of Maryland - Department of Finance

Saikat Nandi

Federal National Mortgage Association (Fannie Mae)

Abstract

Proposals to introduce derivatives whose payouts are explicitly linked to the volatility of an underlying asset have been around for some time. In response to these proposals, a few papers have tried to develop valuation formulae for volatility derivatives ? derivatives that essentially help investors hedge the unpredictable volatility risk. This paper contributes to this nascent literature by developing closed-form/analytical formulae for prices of options and futures on volatility as well as volatility swaps. The primary contribution of this paper is that, unlike all other models, our model is empirically viable and can be easily implemented.

More specifically, our model distinguishes itself from other proposed solutions/models in the following respects: (1) Although volatility is stochastic, it is an exact function of the observed path of asset prices. This is crucial in practice because nonobservability of volatility makes it very difficult, (in fact, impossible) to arrive at prices and hedge ratios of volatility derivatives in an internally consistent fashion, as it is akin to not knowing the stock price when trying to price an equity derivative. (2) The model does not require an unobserved volatility risk premium, nor is it predicated on the strong assumption of the existence of a continuum of options of all strikes and maturities as in some papers. (3) We show how it is possible to replicate (delta hedge) volatility derivatives by trading only in the underlying asset (on whose volatility the derivative exists) and a risk-free asset. This bypasses the problem of having to trade numerously many options on the underlying asset, a hedging strategy proposed in some other models.

Keywords: volatility, options, hedge

JEL Classification: G12, G13

Suggested Citation

Heston, Steven L. and Nandi, Saikat, Derivatives on Volatility: Some Simple Solutions Based on Observables. Federal Reserve Bank of Atlanta WP No. 2000-20, November 2000, Available at SSRN: https://ssrn.com/abstract=249173 or http://dx.doi.org/10.2139/ssrn.249173

Steven L. Heston (Contact Author)

University of Maryland - Department of Finance ( email )

Robert H. Smith School of Business
Van Munching Hall
College Park, MD 20742
United States

Saikat Nandi

Federal National Mortgage Association (Fannie Mae) ( email )

3900 Wisconsin Avenue, NW
Washington, DC 20016-2892
United States
(202)752-8421 (Phone)

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