Fast Calibration of the Affine and Quadratic Models

42 Pages Posted: 25 Aug 2007 Last revised: 19 May 2016

See all articles by Daniel Alexandre Bloch

Daniel Alexandre Bloch

Université Paris VI Pierre et Marie Curie

Date Written: May 1, 2016

Abstract

Using the recent work of Alos and Ewald on option pricing approximations we extend their approach to some specific jump-diffusion models with stochastic interest rates, compute the Greeks and improve the accuracy of the approximations. Further, we obtain analytical solutions to the price of variance swap and volatility swap. Using these results we derive approximations to the equivalent implied volatility surface, and we relate the at-the-money forward term-structure of the surface when the correlation is set to zero to the volatility swap. To conclude we use in the FFT both a change of variable and the approximated call prices as control variates in the computation of more general jump-diffusion models, reducing the variance, making the call price square integrable and drastically increasing the speed of convergence.

Keywords: calibration, option pricing approximations, jump-diffusion models, Malliavin calculus

Suggested Citation

Bloch, Daniel Alexandre, Fast Calibration of the Affine and Quadratic Models (May 1, 2016). Available at SSRN: https://ssrn.com/abstract=1009327 or http://dx.doi.org/10.2139/ssrn.1009327

Daniel Alexandre Bloch (Contact Author)

Université Paris VI Pierre et Marie Curie ( email )

175 Rue du Chevaleret
Paris, 75013
France

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