Journal of Computational Finance
ISSN:
1460-1559 (print)
1755-2850 (online)
Editor-in-chief: Christoph Reisinger
![Risk.net](https://www.risk.net/sites/default/files/styles/print_logo/public/2018-09/print-logo.png?itok=1TpHrpuP)
Pricing options on realized variance in the Heston model with jumps in returns and volatility
Artur Sepp
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.
Copyright Infopro Digital Limited. All rights reserved.
As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (point 2.4), printing is limited to a single copy.
If you would like to purchase additional rights please email info@risk.net
Copyright Infopro Digital Limited. All rights reserved.
You may share this content using our article tools. As outlined in our terms and conditions, https://www.infopro-digital.com/terms-and-conditions/subscriptions/ (clause 2.4), an Authorised User may only make one copy of the materials for their own personal use. You must also comply with the restrictions in clause 2.5.
If you would like to purchase additional rights please email info@risk.net