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Risk-neutral Modeling with Affine and Nonaffine Models

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  • Garland B. Durham

Abstract

Option prices provide a great deal of information regarding the market's expectations of future asset price dynamics. But, the implied dynamics are under the risk-neutral measure rather than the physical measure under which the price of the underlying asset itself evolves. This article demonstrates new techniques for joint analysis of the physical and risk-neutral models using data from both the underlying asset and options. While much of the prior work in this area has focused on affine and affine-jump models because of their analytical tractability, the techniques used in this article are straightforward to apply to a broad class of models of potential interest. The techniques are based on evaluating various integrals of interest using Monte Carlo sums over simulated volatility paths. In an application using S&P 500 index data, we find that log volatility models perform dramatically better than affine models, but that some evidence of misspecification remains. Copyright The Author, 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com, Oxford University Press.

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  • Garland B. Durham, 2013. "Risk-neutral Modeling with Affine and Nonaffine Models," Journal of Financial Econometrics, Oxford University Press, vol. 11(4), pages 650-681, September.
    • Handle: RePEc:oup:jfinec:v:11:y:2013:i:4:p:650-681
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbt009
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    Cited by:

    1. Yoo, Eun Gyu & Yoon, Sun-Joong, 2020. "CBOE VIX and Jump-GARCH option pricing models," International Review of Economics & Finance, Elsevier, vol. 69(C), pages 839-859.
    2. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2017. "Equity index variance: Evidence from flexible parametric jump–diffusion models," Journal of Banking & Finance, Elsevier, vol. 83(C), pages 85-103.
    3. Bardgett, Chris & Gourier, Elise & Leippold, Markus, 2019. "Inferring volatility dynamics and risk premia from the S&P 500 and VIX markets," Journal of Financial Economics, Elsevier, vol. 131(3), pages 593-618.
    4. Gudkov, Nikolay & Ignatieva, Katja, 2021. "Electricity price modelling with stochastic volatility and jumps: An empirical investigation," Energy Economics, Elsevier, vol. 98(C).
    5. Wan, Xiangwei & Yang, Nian, 2021. "Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    6. Xinyu WU & Hailin ZHOU, 2016. "GARCH DIFFUSION MODEL, iVIX, AND VOLATILITY RISK PREMIUM," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(1), pages 327-342.
    7. 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.
    8. Amengual, Dante & Xiu, Dacheng, 2018. "Resolution of policy uncertainty and sudden declines in volatility," Journal of Econometrics, Elsevier, vol. 203(2), pages 297-315.
    9. Park, Yang-Ho, 2020. "Variance disparity and market frictions," Journal of Econometrics, Elsevier, vol. 214(2), pages 326-348.

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