Journal of Computational Finance

Risk.net

Fourier transform algorithms for pricing and hedging discretely sampled exotic variance products and volatility derivatives under additive processes

Wendong Zheng and Yue Kuen Kwok

ABSTRACT

We develop efficient fast Fourier transform algorithms for pricing and hedging discretely sampled variance products and volatility derivatives under additive processes (time-inhomogeneous Lévy processes). Our numerical algorithms are nontrivial versions of the Fourier space time-stepping method to nonlinear path-dependent payoff structures, like those in variance products and volatility derivatives. The exotic path dependency associated with the discretely sampled realized variance is captured in the numerical procedure by updating two pathdependent state variables across monitoring dates. The time-stepping procedure between successive monitoring dates can be performed using fast Fourier transform calculations without the usual tedious time-stepping calculations in typical finite-difference algorithms. We also derive effective numerical procedures that compute the hedge parameters of variance products and volatility derivatives. Numerical tests on pricing various variance products and volatility derivatives were performed to illustrate the efficiency, accuracy, reliability and robustness of the proposed Fourier transform algorithms.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here