IDEAS home Printed from https://ideas.repec.org/p/hhb/aarbfi/2009-05.html
   My bibliography  Save this paper

A Consistent Pricing Model for Index Options and Volatility Derivatives

Author

Listed:
  • Cont, Rama

    (Center for Financial Engineering)

  • Kokholm, Thomas

    (Department of Business Studies, Aarhus School of Business)

Abstract

We propose and study a flexible modeling framework for the joint dynamics of an index and a set of forward variance swap rates written on this index, allowing options on forward variance swaps and options on the underlying index to be priced consistently. Our model reproduces various empirically observed properties of variance swap dynamics and allows for jumps in volatility and returns. An affine specification using L´evy processes as building blocks leads to analytically tractable pricing formulas for options on variance swaps as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index. The calibration of the model is done in two steps, first by matching VIX option prices and then by matching prices of options on the underlying

Suggested Citation

  • Cont, Rama & Kokholm, Thomas, 2009. "A Consistent Pricing Model for Index Options and Volatility Derivatives," Finance Research Group Working Papers F-2009-05, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    • Handle: RePEc:hhb:aarbfi:2009-05
    as

    Download full text from publisher

    File URL: http://www.hha.dk/afl/wp/fin/F_2009_05.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rama Cont, 2008. "Frontiers in Quantitative Finance: credit risk and volatility modeling," Post-Print hal-00437588, HAL.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gianna Figa-Talamanca & Maria Letizia Guerra, 2012. "Market Application of the Fuzzy-Stochastic Approach in the Heston Option Pricing Model," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(2), pages 162-179, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    2. H. Peter Boswijk & Roger J. A. Laeven & Evgenii Vladimirov, 2022. "Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation," Papers 2210.06217, arXiv.org.
    3. Diego Amaya & Jean-François Bégin & Geneviève Gauthier, 2022. "The Informational Content of High-Frequency Option Prices," Management Science, INFORMS, vol. 68(3), pages 2166-2201, March.
    4. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    5. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    6. Dario Alitab & Giacomo Bormetti & Fulvio Corsi & Adam A. Majewski, 2019. "A realized volatility approach to option pricing with continuous and jump variance components," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 639-664, December.
    7. Leunga Njike, Charles Guy & Hainaut, Donatien, 2024. "Affine Heston model style with self-exciting jumps and long memory," LIDAM Discussion Papers ISBA 2024001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Zura Kakushadze, 2016. "Volatility Smile as Relativistic Effect," Papers 1610.02456, arXiv.org, revised Feb 2017.
    9. Boris Ter-Avanesov & Homayoon Beigi, 2024. "MLP, XGBoost, KAN, TDNN, and LSTM-GRU Hybrid RNN with Attention for SPX and NDX European Call Option Pricing," Papers 2409.06724, arXiv.org, revised Oct 2024.
    10. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    11. Maekawa, Koichi & Lee, Sangyeol & Morimoto, Takayuki & Kawai, Ken-ichi, 2008. "Jump diffusion model with application to the Japanese stock market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(2), pages 223-236.
    12. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
    13. Duy Nguyen, 2018. "A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-30, December.
    14. Jimin Lin & Guixin Liu, 2024. "Neural Term Structure of Additive Process for Option Pricing," Papers 2408.01642, arXiv.org, revised Oct 2024.
    15. Rong Du & Duy-Minh Dang, 2023. "Fourier Neural Network Approximation of Transition Densities in Finance," Papers 2309.03966, arXiv.org, revised Sep 2024.
    16. Chen, Si & Zhou, Zhen & Li, Shenghong, 2016. "An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach," Economic Modelling, Elsevier, vol. 58(C), pages 655-664.
    17. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    18. Kilic, Erdem, 2017. "Contagion effects of U.S. Dollar and Chinese Yuan in forward and spot foreign exchange markets," Economic Modelling, Elsevier, vol. 62(C), pages 51-67.
    19. Fang, Fang & Oosterlee, Kees, 2008. "Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions," MPRA Paper 9248, University Library of Munich, Germany.
    20. Guo, Jingjun & Kang, Weiyi & Wang, Yubing, 2024. "Multi-perspective option price forecasting combining parametric and non-parametric pricing models with a new dynamic ensemble framework," Technological Forecasting and Social Change, Elsevier, vol. 204(C).

    More about this item

    Keywords

    No keywords;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhb:aarbfi:2009-05. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Helle Vinbaek Stenholt (email available below). General contact details of provider: https://edirc.repec.org/data/ifhhadk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.