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Pricing Options on Realized Volatility in Heston Model with Volatility Jumps

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Artur Sepp 

The Heston stochastic volatility model with volatility jumps can serve as a good tool for pricing and risk-managing derivatives on realized volatility and variance. In this paper, we derive analytical and approximate solutions for the values of contingent claims on realized variance and volatility under the Heston model with volatility jumps. By employing generalized Fourier transform we obtain analytical solutions (up to numerical inversion of Fourier integral) for swaps on realized volatility and variance with floor and cap protections, and for options on realized variance and volatility swaps. We also consider pricing forward-start claims on realized variance and volatility, including options on VIX, and obtain a closed-form solution and an accurate convexity adjustment formula for pricing these claims. Our solutions allow to unify pricing and risk managing of many volatility-dependent claims into one single framework. In addition, we derive a log-normal approximation to the density of the realized variance in the Heston model and obtain accurate approximate solutions for volatility- and variance-dependent claims with longer maturities.

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Submitter: vanna
Publisher: malbury
Published: Sat, 08-Sep-2007
ICRA: EC - Early Childhood
linked: 1940 times

Rating:    (6 Votes)
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