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Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants

Author

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  • Brignone, Riccardo
  • Gonzato, Luca
  • Lütkebohmert, Eva

Abstract

We propose a general, accurate and fast econometric approach for the estimation of affine option pricing models. The algorithm belongs to the class of Laplace-Type Estimation (LTE) techniques and exploits Sequential Monte Carlo (SMC) methods. We employ functions of the risk-neutral cumulants given in closed form to marginalize latent states, and we address parameter estimation by designing a density tempered SMC sampler. We test our algorithm on simulated data by tackling the challenging inference problem of estimating an option pricing model which displays two stochastic volatility factors, allows for co-jumps between price and volatility, and stochastic jump intensity. Furthermore, we consider real data and estimate the model on a large panel of option prices. Numerical studies confirm the accuracy of our estimates and the superiority of the proposed approach compared to its natural benchmark.

Suggested Citation

  • Brignone, Riccardo & Gonzato, Luca & Lütkebohmert, Eva, 2023. "Efficient Quasi-Bayesian Estimation of Affine Option Pricing Models Using Risk-Neutral Cumulants," Journal of Banking & Finance, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:jbfina:v:148:y:2023:i:c:s0378426622003259
    DOI: 10.1016/j.jbankfin.2022.106745
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    as
    1. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436, June.
    2. Fulop, Andras & Li, Junye, 2013. "Efficient learning via simulation: A marginalized resample-move approach," Journal of Econometrics, Elsevier, vol. 176(2), pages 146-161.
    3. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    4. A. S. Hurn & K. A. Lindsay & A. J. McClelland, 2015. "Estimating the Parameters of Stochastic Volatility Models Using Option Price Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 579-594, October.
    5. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    6. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    7. Bruno Feunou & Cédric Okou, 2018. "Risk‐neutral moment‐based estimation of affine option pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 1007-1025, November.
    8. Hainaut, D. & Moraux, F., 2017. "Hedging of options in presence of jump clustering," LIDAM Discussion Papers ISBA 2017012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Gonzato, Luca & Sgarra, Carlo, 2021. "Self-exciting jumps in the oil market: Bayesian estimation and dynamic hedging," Energy Economics, Elsevier, vol. 99(C).
    10. Friedrich Hubalek & Martin Keller-Ressel & Carlo Sgarra, 2017. "Geometric Asian option pricing in general affine stochastic volatility models with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 17(6), pages 873-888, June.
    11. Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor, 2015. "The risk premia embedded in index options," Journal of Financial Economics, Elsevier, vol. 117(3), pages 558-584.
    12. Todorov, Viktor, 2011. "Econometric analysis of jump-driven stochastic volatility models," Journal of Econometrics, Elsevier, vol. 160(1), pages 12-21, January.
    13. 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.
    14. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    15. N. Chopin & P. E. Jacob & O. Papaspiliopoulos, 2013. "SMC-super-2: an efficient algorithm for sequential analysis of state space models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 397-426, June.
    16. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    17. Johannes Rauch & Carol Alexander, 2016. "Tail Risk Premia for Long-Term Equity Investors," Papers 1602.00865, arXiv.org.
    18. Yin, Weiwei & Li, Junye, 2014. "Macroeconomic fundamentals and the exchange rate dynamics: A no-arbitrage macro-finance approach," Journal of International Money and Finance, Elsevier, vol. 41(C), pages 46-64.
    19. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    20. Du Du & Dan Luo, 2019. "The Pricing of Jump Propagation: Evidence from Spot and Options Markets," Management Science, INFORMS, vol. 67(5), pages 2360-2387, May.
    21. Brix, Anne Floor & Lunde, Asger & Wei, Wei, 2018. "A generalized Schwartz model for energy spot prices — Estimation using a particle MCMC method," Energy Economics, Elsevier, vol. 72(C), pages 560-582.
    22. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    23. repec:dau:papers:123456789/7305 is not listed on IDEAS
    24. Riccardo Brignone & Carlo Sgarra, 2020. "Asian options pricing in Hawkes-type jump-diffusion models," Annals of Finance, Springer, vol. 16(1), pages 101-119, March.
    25. Junye Li & Gabriele Zinna, 2018. "The Variance Risk Premium: Components, Term Structures, and Stock Return Predictability," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 411-425, July.
    26. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    27. Claudia Yeap & Simon S Kwok & S T Boris Choy, 2018. "A Flexible Generalized Hyperbolic Option Pricing Model and Its Special Cases," Journal of Financial Econometrics, Oxford University Press, vol. 16(3), pages 425-460.
    28. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    29. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    30. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    31. 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.
    32. Jessica A. Wachter, 2013. "Can Time-Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?," Journal of Finance, American Finance Association, vol. 68(3), pages 987-1035, June.
    33. Jin-Chuan Duan & Andras Fulop, 2015. "Density-Tempered Marginalized Sequential Monte Carlo Samplers," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 192-202, April.
    34. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.
    35. Ruge-Murcia, Francisco, 2012. "Estimating nonlinear DSGE models by the simulated method of moments: With an application to business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 914-938.
    36. Bruno Feunou & Ricardo Lopez Aliouchkin & Roméo Tedongap & Lai Xi, 2017. "Variance Premium, Downside Risk and Expected Stock Returns," Staff Working Papers 17-58, Bank of Canada.
    37. Roman Kozhan & Anthony Neuberger & Paul Schneider, 2013. "The Skew Risk Premium in the Equity Index Market," The Review of Financial Studies, Society for Financial Studies, vol. 26(9), pages 2174-2203.
    38. Andras Fulop & Junye Li & Jun Yu, 2015. "Self-Exciting Jumps, Learning, and Asset Pricing Implications," The Review of Financial Studies, Society for Financial Studies, vol. 28(3), pages 876-912.
    39. Fulop, Andras & Li, Junye, 2019. "Bayesian estimation of dynamic asset pricing models with informative observations," Journal of Econometrics, Elsevier, vol. 209(1), pages 114-138.
    40. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    More about this item

    Keywords

    Sequential Monte Carlo; Quasi-Bayesian Estimation; Risk-Neutral Cumulants; Multifactor Affine Models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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