Fast Calibration of the Affine and Quadratic Models
42 Pages Posted: 25 Aug 2007 Last revised: 19 May 2016
Date Written: May 1, 2016
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
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