Orthogonal Expansions for VIX Options Under Affine Jump Diffusions

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Orthogonal Expansions for VIX Options Under Affine Jump Diffusions. / Barletta, Andrea; Nicolato, Elisa.

In: Quantitative Finance, Vol. 18, No. 6, 2018, p. 951-967.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Author

Barletta, Andrea ; Nicolato, Elisa. / Orthogonal Expansions for VIX Options Under Affine Jump Diffusions. In: Quantitative Finance. 2018 ; Vol. 18, No. 6. pp. 951-967.

Bibtex

@article{370905207da846729a90ffc28b9d2d47,

title = "Orthogonal Expansions for VIX Options Under Affine Jump Diffusions",

abstract = "In this work we derive new closed–form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel. Orthogonal expansions based on the Gaussian distribution, such as Edgeworth or Gram–Charlier expansions, have been successfully employed by a number of authors in the context of equity options. However, these expansions are not quite suitable for volatility or variance densities as they inherently assign positive mass to the negative real line. Here we approximate option prices via expansions that instead are based on kernels defined on the positive real line. Specifically, we consider a flexible family of distributions, which generalizes the gamma kernel associated with the classic Laguerre expansions. The method can be employed whenever the moments of the underlying variance distribution are known. It provides fast and accurate price computations, and therefore it represents a valid and possibly more robust alternative to pricing techniques based on Fourier transform inversions.",

keywords = "APPROXIMATIONS, Affine jump diffusion, IMPACT, Laguerre expansions, MODELS, Orthogonal polynomials, PRICES, RISK, STOCHASTIC VOLATILITY, VALUATION, VARIANCE, VIX options",

author = "Andrea Barletta and Elisa Nicolato",

year = "2018",

doi = "10.1080/14697688.2017.1371322",

language = "English",

volume = "18",

pages = "951--967",

journal = "Quantitative Finance",

issn = "1469-7688",

publisher = "Routledge",

number = "6",

}

RIS

TY - JOUR

T1 - Orthogonal Expansions for VIX Options Under Affine Jump Diffusions

AU - Barletta, Andrea

AU - Nicolato, Elisa

PY - 2018

Y1 - 2018

N2 - In this work we derive new closed–form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel. Orthogonal expansions based on the Gaussian distribution, such as Edgeworth or Gram–Charlier expansions, have been successfully employed by a number of authors in the context of equity options. However, these expansions are not quite suitable for volatility or variance densities as they inherently assign positive mass to the negative real line. Here we approximate option prices via expansions that instead are based on kernels defined on the positive real line. Specifically, we consider a flexible family of distributions, which generalizes the gamma kernel associated with the classic Laguerre expansions. The method can be employed whenever the moments of the underlying variance distribution are known. It provides fast and accurate price computations, and therefore it represents a valid and possibly more robust alternative to pricing techniques based on Fourier transform inversions.

AB - In this work we derive new closed–form pricing formulas for VIX options in the jump-diffusion SVJJ model proposed by Duffie et al. (2000). Our approach is based on the classic methodology of approximating a density function with an orthogonal expansion of polynomials weighted by a kernel. Orthogonal expansions based on the Gaussian distribution, such as Edgeworth or Gram–Charlier expansions, have been successfully employed by a number of authors in the context of equity options. However, these expansions are not quite suitable for volatility or variance densities as they inherently assign positive mass to the negative real line. Here we approximate option prices via expansions that instead are based on kernels defined on the positive real line. Specifically, we consider a flexible family of distributions, which generalizes the gamma kernel associated with the classic Laguerre expansions. The method can be employed whenever the moments of the underlying variance distribution are known. It provides fast and accurate price computations, and therefore it represents a valid and possibly more robust alternative to pricing techniques based on Fourier transform inversions.

KW - APPROXIMATIONS

KW - Affine jump diffusion

KW - IMPACT

KW - Laguerre expansions

KW - MODELS

KW - Orthogonal polynomials

KW - PRICES

KW - RISK

KW - STOCHASTIC VOLATILITY

KW - VALUATION

KW - VARIANCE

KW - VIX options

UR - http://www.scopus.com/inward/record.url?scp=85030718734&partnerID=8YFLogxK

U2 - 10.1080/14697688.2017.1371322

DO - 10.1080/14697688.2017.1371322

M3 - Journal article

VL - 18

SP - 951

EP - 967

JO - Quantitative Finance

JF - Quantitative Finance

SN - 1469-7688

IS - 6

ER -

Department of Economics and Business Economics