Abstract
We have seen that modeling the logarithmic returns of the underlying as a Brownian motion does not capture the rich structure observed in the option markets. It can explain neither the skew or smile nor the dynamics of the implied volatility surface. As an attempt at improvement, we extended the Black–Scholes model in the previous two chapters to local volatility models and stochastic volatility models. Despite the success and frequent use of these model types around financial institutions, we have made it clear that they also suffer from the fact that the dynamics disagree with market behavior. For this reason we now discuss yet another model class generalizing the Black–Scholes framework.
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References
Barndorff-Nielsen OE, Halgreen C (1977) Infinite divisibility of the hyperbolic and generalized inverse Gaussian distributions. Z Wahrscheinlichkeitstheorie verwandte Geb 38:309–312
Barndorff-Nielsen OE, Shephard N (2001) Non-Gaussian OU based models and some of their uses in financial economics. J Roy Stat Soc Ser B 63:167–241
Bates D (1996) Jumps and stochastic volatility: The exchange rate processes implicit in Deutschemark options. Rev Financial Stud 9:69–107
Carr P, Geman H, Madan D, Yor M (2002) The fine structure of asset returns: an empirical investigation. J Bus 75:305–332
Carr P, Geman H, Madan D, Yor M (2004) From local volatility to local Lévy models. Quant Finance 5:581–588
Madan DB, Carr P, Chang EC (1998) The variance gamma process and option pricing. Eur Finance Rev 2:79–105
Watson GN (1995) A treatise on the theory of bessel functions. Cambridge University Press, Cambridge
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© 2011 Springer-Verlag Berlin Heidelberg
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Ekstrand, C. (2011). Lévy Models. In: Financial Derivatives Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22155-2_8
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DOI: https://doi.org/10.1007/978-3-642-22155-2_8
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