Pricing options on realized variance in the Heston model with jumps in returns and volatility

Artur Sepp

Journal of Computational Finance

Abstract: ABSTRACT We develop analytical methodology for pricing and hedging options on the realized variance under the Heston stochastic variance model (1993) augmented with jumps in asset returns and variance. By employing a generalized Fourier transform we obtain analytical solutions (up to numerical inversion of the Fourier integral) for swaps on the realized volatility and variance and for options on these swaps. We also extend our framework for pricing forward start options on the realized variance and volatility, including options on the VIX (the Chicago Board Options Exchange Volatility Index). Our methodology allows us to consistently unify pricing and risk management of different volatility options. We provide an example of model parameter estimation using both time series of the VIX and the VIX options data and find that the proposed model is in agreement with both historical and implied market data. Finally, we derive a lognormal approximation to the density of the realized variance in the Heston model and obtain accurate approximate solutions for volatility options with longer maturities.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... turns-and-volatility (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rsk:journ0:2160414

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().