A simple closed-form formula for pricing discretely-sampled variance swaps under the heston model

Sanae Rujivan, Song-Ping Zhu


We develop a simplified analytical approach for pricing discretely-sampled variance swaps with the realized variance, defined in terms of the squared log return of the underlying price. The closed-form formula obtained for Heston’s two-factor stochastic volatility model is in a much simpler form than those proposed in literature. Most interestingly, we discuss the validity of our solution as well as some other previous solutions in different forms in the parameter space. We demonstrate that market practitioners need to be cautious, making sure that their model parameters extracted from market data are in the right parameter subspace, when any of these analytical pricing formulae is adopted to calculate the fair delivery price of a discretely-sampled variance swap.



variance swaps; Heston model; closed-form exact solution; stochastic volatility

DOI: http://dx.doi.org/10.21914/anziamj.v56i0.7455

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.