Asymptotic formulae for implied volatility in the Heston model

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Forde, Martin; Jacquier, Antoine; Mijatovic, Aleksandar;
(2009)

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The pr... View more
  • References (33)
    33 references, page 1 of 4

    [1] Ait-Sahalia, Y. & Yu, J. 2006 Saddlepoint Approximations for Continuous-Time Markov Processes. Journal of Econometrics, 134, 507-551. (doi:10.1016/j.jeconom.2005.07.004).

    [2] Albrecher, H., Mayer, P., Schoutens, W. & Tistaert, J. 2007 The Little Heston Trap. Wilmott Magazine, January issue, 83-92.

    [3] Andersen, L.B.G. & Piterbarg, V.V. 2007 Moment Explosions in Stochastic Volatility Models. Finance & Stochastics 11 (1), 29-50. (doi: 10.1007/s00780-006-0011-7).

    [4] Benaim, S. & Friz, P. 2009 Regular Variation and Smile Asymptotics. Mathematical Finance 19 (1), 1-12. (doi:10.1111/j.1467-9965.2008.00354).

    [5] Benaim, S. & Friz, P. 2008 Smile Asymptotics 2: Models with Known Moment Generating Functions. Journal of Applied Probability 45 (1), 16-32. (doi:10.1239/jap/1208358948).

    [6] Berestycki, H., Busca, J. & Florent, I. 2004 Computing the Implied Volatility in Stochastic Volatility models. Comm. Pure App. Math. 57 (10), 1352-1373. (doi:10.1002/cpa.20039).

    [7] Bleistein, N. & Handelsman, R.A. 1975 Asymptotic expansions of integrals. New York, London, Holt, Rinehart and Winston.

    [8] Butler, R.W. 2007 Saddlepoint Approximations with Applications. Cambridge University Press.

    [9] Carr, P. & Madan, D. 2009 Saddlepoint Methods for Option Pricing. Journ. Comp. Fin. 13 (1), 49-62.

    [10] Feng, J., Forde, M. & Fouque, J.P. 2009 Short maturity asymptotics for a fast meanreverting Heston stochastic volatility model. SIAM Journal of Financial Mathematics 1, 126-141. (doi:10.1137/090745465).

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