Options Valuation and Calibration for Leveraged Exchange-Traded Funds with Heston-Nandi and Inverse Gaussian GARCH Models

Cao, Hongkai; Chatterjee, Rupak; Cui, Zhenyu

doi:10.2139/ssrn.3302338

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Volatility Derivatives Valuation Framework1

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2020

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“…To determine the conditional expectation for VIX call payoff (22), we have to obtain the transitional probability density function of the conditional variance. This transition probability density function can be derived through the Fourier inversion of the characteristic function, using the so‐called Gil‐Pelaez's inversion theorem (see Cao, Chatterjee, & Cui, 2019; Gil‐Pelaez, 1951). The VIX option pricing formula is illustrated in the following proposition.…”

Section: Volatility Derivatives Valuation Frameworkmentioning

confidence: 99%

Valuation of VIX and target volatility options with affine GARCH models

Cao

Badescu

Cui

et al. 2020

Journal of Futures Markets

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In this paper we propose semiclosed‐form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte–Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options.

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Section: Volatility Derivatives Valuation Frameworkmentioning

confidence: 99%