Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach

Elisa Alòs () and Kenichiro Shiraya ()
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Elisa Alòs: Universitat Pompeu Fabra
Kenichiro Shiraya: The University of Tokyo

Finance and Stochastics, 2019, vol. 23, issue 2, No 5, 423-447

Abstract: Abstract This paper is devoted to studying the difference between the fair strike of a volatility swap and the at-the-money implied volatility (ATMI) of a European call option. It is well known that the difference between these two quantities converges to zero as the time to maturity decreases. In this paper, we make use of a Malliavin calculus approach to derive an exact expression for this difference. This representation allows us to establish that the order of convergence is different in the correlated and uncorrelated cases, and that it depends on the behavior of the Malliavin derivative of the volatility process. In particular, we see that for volatilities driven by a fractional Brownian motion, this order depends on the corresponding Hurst parameter H $H$ . Moreover, in the case H ≥ 1 / 2 $H\geq 1/2$ , we develop a model-free approximation formula for the volatility swap in terms of the ATMI and its skew.

Keywords: Malliavin calculus; Fractional volatility models; Volatility swaps; 91G60; 91G80; 60H07 (search for similar items in EconPapers)
JEL-codes: C6 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (12)

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DOI: 10.1007/s00780-019-00384-5

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