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Pricing Cryptocurrency options: the case of CRIX and Bitcoin

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  • Chen, Cathy Yi-Hsuan
  • Härdle, Wolfgang Karl
  • Hou, Ai Jun
  • Wang, Weining

Abstract

The CRIX (CRyptocurrency IndeX) has been constructed based on a number of cryptos and provides a high coverage of market liquidity, hu.berlin/crix. The crypto currency market is a new asset market and attracts a lot of investors recently. Surprisingly a market for contingent claims hat not been built up yet. A reason is certainly the lack of pricing tools that are based on solid financial econometric tools. Here a first step towards pricing of derivatives of this new asset class is presented. After a careful econometric pre-analysis we motivate an affine jump diffusion model, i.e., the SVCJ (Stochastic Volatility with Correlated Jumps) model. We calibrate SVCJ by MCMC and obtain interpretable jump processes and then via simulation price options. The jumps present in the cryptocurrency fluctutations are an essential component. Concrete examples are given to establish an OCRIX exchange platform trading options on CRIX.

Suggested Citation

  • Chen, Cathy Yi-Hsuan & Härdle, Wolfgang Karl & Hou, Ai Jun & Wang, Weining, 2018. "Pricing Cryptocurrency options: the case of CRIX and Bitcoin," IRTG 1792 Discussion Papers 2018-004, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
  • Handle: RePEc:zbw:irtgdp:2018004
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    References listed on IDEAS

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    1. Pavel Ciaian & Miroslava Rajcaniova & d’Artis Kancs, 2016. "The economics of BitCoin price formation," Applied Economics, Taylor & Francis Journals, vol. 48(19), pages 1799-1815, April.
    2. Jamal Bouoiyour & Refk Selmi & Aviral Kumar Tiwari & Olaolu Richard Olayeni, 2016. "What drives Bitcoin price?," Economics Bulletin, AccessEcon, vol. 36(2), pages 843-850.
    3. Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
    4. Asgharian, Hossein & Nossman, Marcus, 2011. "Risk contagion among international stock markets," Journal of International Money and Finance, Elsevier, vol. 30(1), pages 22-38, February.
    5. Simon Trimborn & Wolfgang Karl Härdle, 2015. "CRIX or evaluating Blockchain based currencies," SFB 649 Discussion Papers SFB649DP2015-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    7. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    8. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    9. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    10. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    11. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    12. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, June.
    13. Trimborn, Simon & Härdle, Wolfgang Karl, 2018. "CRIX an Index for cryptocurrencies," Journal of Empirical Finance, Elsevier, vol. 49(C), pages 107-122.
    14. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    15. 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.
    16. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    17. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    18. Hossein Asgharian & Christoffer Bengtsson, 2006. "Jump Spillover in International Equity Markets," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 167-203.
    19. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    20. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
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    Citations

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    Cited by:

    1. da Gama Silva, Paulo Vitor Jordão & Klotzle, Marcelo Cabus & Pinto, Antonio Carlos Figueiredo & Gomes, Leonardo Lima, 2019. "Herding behavior and contagion in the cryptocurrency market," Journal of Behavioral and Experimental Finance, Elsevier, vol. 22(C), pages 41-50.
    2. Chen, Cathy Yi-Hsuan & Després, Roméo & Guo, Li & Renault, Thomas, 2019. "What makes cryptocurrencies special? Investor sentiment and return predictability during the bubble," IRTG 1792 Discussion Papers 2019-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Alessandra Cretarola & Gianna Figà-Talamanca & Cyril Grunspan, 2021. "Blockchain and cryptocurrencies: economic and financial research," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 781-787, December.
    4. Junjie Hu & Wolfgang Karl Hardle & Weiyu Kuo, 2019. "Risk of Bitcoin Market: Volatility, Jumps, and Forecasts," Papers 1912.05228, arXiv.org, revised Dec 2021.
    5. Pele, Daniel Traian & Mazurencu-Marinescu-Pele, Miruna, 2018. "Cryptocurrencies, Metcalfe's law and LPPL models," IRTG 1792 Discussion Papers 2018-056, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    6. Wolfgang Karl Härdle & Campbell R Harvey & Raphael C G Reule, 2020. "Understanding Cryptocurrencies," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 18(2), pages 181-208.
    7. Fabian Woebbeking, 2021. "Cryptocurrency volatility markets," Digital Finance, Springer, vol. 3(3), pages 273-298, December.
    8. Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2019. "Advanced model calibration on bitcoin options," Digital Finance, Springer, vol. 1(1), pages 117-137, November.
    9. Christian Conrad & Anessa Custovic & Eric Ghysels, 2018. "Long- and Short-Term Cryptocurrency Volatility Components: A GARCH-MIDAS Analysis," JRFM, MDPI, vol. 11(2), pages 1-12, May.
    10. Pele, Daniel Traian & Mazurencu-Marinescu-Pele, Miruna, 2019. "Metcalfe's law and herding behaviour in the cryptocurrencies market," Economics Discussion Papers 2019-16, Kiel Institute for the World Economy (IfW Kiel).
    11. Alessandra Cretarola & Gianna Figà-Talamanca, 2021. "Detecting bubbles in Bitcoin price dynamics via market exuberance," Annals of Operations Research, Springer, vol. 299(1), pages 459-479, April.

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    More about this item

    Keywords

    CRyptocurrency IndeX; CRIX; Bitcoin; Cryptocurrency; SVCJ; Option pricing; OCRIX;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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