Fast Option Pricing for Calibration Without Closed-Form Cumulants

Summary

The document asks how to price options quickly during model calibration, comparing the Carr–Madan and COS methods. It highlights Variance Gamma models with stochastic arrivals and related models where cumulants may not be available in closed form. The central question is how to calculate those cumulants in that setting, or which alternative algorithm can provide fast option prices.

No answer, derivation, benchmark, or recommended method is included. The excerpt therefore identifies a practical numerical challenge rather than resolving it: calibration needs repeated option valuations, while some candidate models complicate methods that rely on cumulants. It does not compare speed or accuracy, explain numerical implementation, or state whether cumulants can be approximated or obtained by another technique.

Key ideas

• Option calibration can require fast repeated price calculations.
• The question compares Carr–Madan and COS pricing methods.
• Some Variance Gamma models with stochastic arrivals lack cumulants in closed form.
• The excerpt provides no method, comparison, or recommendation for handling that limitation.

Tags

# Carr-madan vs COS method vs other methods


# Carr-madan vs COS method vs other methods












Hey during calibration we have to calculate option prices very fast. The most popular method was developed by Carr-Madan, but COS method also is very popular. The problem is for example with Variance Gamma with Stochastic arrival model and other models of this type, where we don't know the cumulants in closed form. How to calculate these cumulants in such a situation, or what other algorithm do you recommend for quick calculation of option prices?

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