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Level and slope of volatility smiles in long-run risk models

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  • Branger, Nicole
  • Rodrigues, Paulo
  • Schlag, Christian

Abstract

We propose a long-run risk model with stochastic volatility, a time-varying mean reversion level of volatility, and jumps in the state variables. The special feature of our model is that the jump intensity is not affine in the conditional variance but driven by a separate process. We show that this separation of jump risk from volatility risk is needed to match the empirically weak link between the level and the slope of the implied volatility smile for S&P 500 options.

Suggested Citation

  • Branger, Nicole & Rodrigues, Paulo & Schlag, Christian, 2018. "Level and slope of volatility smiles in long-run risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 86(C), pages 95-122.
    • Handle: RePEc:eee:dyncon:v:86:y:2018:i:c:p:95-122
    DOI: 10.1016/j.jedc.2017.10.007
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    3. Giacomo Toscano & Maria Cristina Recchioni, 2020. "Bias optimal vol-of-vol estimation: the role of window overlapping," Papers 2004.04013, arXiv.org, revised Jul 2021.
    4. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    5. Ruan, Xinfeng, 2020. "Volatility-of-volatility and the cross-section of option returns," Journal of Financial Markets, Elsevier, vol. 48(C).
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    7. Zhang, Qun & Zhang, Zhendong & Luo, Jiawen, 2024. "Asymmetric and high-order risk transmission across VIX and Chinese futures markets," International Review of Financial Analysis, Elsevier, vol. 93(C).
    8. Irina Zviadadze, 2021. "Term Structure of Risk in Expected Returns [Stock returns and volatility: Pricing the short-run and long-run components of market risk]," The Review of Financial Studies, Society for Financial Studies, vol. 34(12), pages 6032-6086.
    9. Min-Ku Lee & See-Woo Kim & Jeong-Hoon Kim, 2022. "Variance Swaps Under Multiscale Stochastic Volatility of Volatility," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 39-64, March.

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    More about this item

    Keywords

    Asset pricing; Epstein–Zin preferences; Jump risk; Stochastic volatility; Level and slope of implied volatility smile;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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