A New Look at Short‐Term Implied Volatility in Asset Price Models with Jumps

35 Pages Posted: 13 Jan 2016

See all articles by Aleksandar Mijatovic

Aleksandar Mijatovic

Imperial College London

Peter Tankov

ENSAE, Institut Polytechnique de Paris

Date Written: January 2016

Abstract

We analyze the behavior of the implied volatility smile for options close to expiry in the exponential Lévy class of asset price models with jumps. We introduce a new renormalization of the strike variable with the property that the implied volatility converges to a nonconstant limiting shape, which is a function of both the diffusion component of the process and the jump activity (Blumenthal–Getoor) index of the jump component. Our limiting implied volatility formula relates the jump activity of the underlying asset price process to the short‐end of the implied volatility surface and sheds new light on the difference between finite and infinite variation jumps from the viewpoint of option prices: in the latter, the wings of the limiting smile are determined by the jump activity indices of the positive and negative jumps, whereas in the former, the wings have a constant model‐independent slope. This result gives a theoretical justification for the preference of the infinite variation Lévy models over the finite variation ones in the calibration based on short‐maturity option prices.

Keywords: exponential Lévy models, Blumenthal–Getoor index, short‐dated options, implied volatility

Suggested Citation

Mijatovic, Aleksandar and Tankov, Peter, A New Look at Short‐Term Implied Volatility in Asset Price Models with Jumps (January 2016). Mathematical Finance, Vol. 26, Issue 1, pp. 149-183, 2016, Available at SSRN: https://ssrn.com/abstract=2714641 or http://dx.doi.org/10.1111/mafi.12055

Aleksandar Mijatovic (Contact Author)

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/a.mijatovic

Peter Tankov

ENSAE, Institut Polytechnique de Paris ( email )

Palaiseau
France

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