ON THE RELATIONSHIP BETWEEN THE CALL PRICE SURFACE AND THE IMPLIED VOLATILITY SURFACE CLOSE TO EXPIRY

Michael Roper () and Marek Rutkowski ()
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Michael Roper: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Marek Rutkowski: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2009, vol. 12, issue 04, 427-441

Abstract: We examine the asymptotic behaviour of the call price surface and the associated Black-Scholes implied volatility surface in the small time to expiry limit under the condition of no arbitrage. In the final section, we examine a related question of existence of a market model with non-convergent implied volatility. We show that there exist arbitrage free markets in which implied volatility may fail to converge to any value, finite or infinite.

Keywords: Option pricing; implied volatility; logarithmic limit; Black-Scholes formula; asymptotic and approximate formulae (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (23)

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DOI: 10.1142/S0219024909005336

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