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Quanto option pricing in the presence of fat tails and asymmetric dependence

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  • Kim, Young Shin
  • Lee, Jaesung
  • Mittnik, Stefan
  • Park, Jiho

Abstract

We present an approach to pricing European quanto options assuming that the underlying instruments follow a multivariate normal tempered stable (NTS) process. This allows for both fat-tailedness and asymmetric dependence between the returns on the underlying asset and the exchange rate. In an empirical application, we estimate the market and risk-neutral parameters for a quanto construction involving the Nikkei 225 index, as the underlying asset, and the Japanese yen and the US dollar exchange rate. While the Gaussian model is clearly rejected by the data, the NTS model cannot be rejected at any reasonable level. A calibration exercise demonstrates that the prices implied by the estimated NTS and the conventional Gaussian models differ substantially, with the NTS model yielding a superior performance as it better reflects the tail properties of the instruments involved.

Suggested Citation

  • Kim, Young Shin & Lee, Jaesung & Mittnik, Stefan & Park, Jiho, 2015. "Quanto option pricing in the presence of fat tails and asymmetric dependence," Journal of Econometrics, Elsevier, vol. 187(2), pages 512-520.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:2:p:512-520
    DOI: 10.1016/j.jeconom.2015.02.035
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    References listed on IDEAS

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    8. Young Kim & Rosella Giacometti & Svetlozar Rachev & Frank Fabozzi & Domenico Mignacca, 2012. "Measuring financial risk and portfolio optimization with a non-Gaussian multivariate model," Annals of Operations Research, Springer, vol. 201(1), pages 325-343, December.
    9. Young Kim & Frank Fabozzi & Zuodong Lin & Svetlozar Rachev, 2012. "Option pricing and hedging under a stochastic volatility Lévy process model," Review of Derivatives Research, Springer, vol. 15(1), pages 81-97, April.
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    Cited by:

    1. Young Shin Kim & Kum-Hwan Roh & Raphael Douady, 2022. "Tempered stable processes with time-varying exponential tails," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 541-561, March.
    2. Lin, Lisha & Li, Yaqiong & Gao, Rui & Wu, Jianhong, 2021. "The numerical simulation of Quanto option prices using Bayesian statistical methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    3. Bošnjak Mile & Novak Ivan & Vlajčić Davor, 2021. "Market Efficiency of Euro Exchange Rates and Trading Strategies," Naše gospodarstvo/Our economy, Sciendo, vol. 67(2), pages 10-19, June.
    4. Gong, Xiaoli & Zhuang, Xintian, 2017. "American option valuation under time changed tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 57-68.
    5. Young Shin Kim, 2022. "Portfolio optimization and marginal contribution to risk on multivariate normal tempered stable model," Annals of Operations Research, Springer, vol. 312(2), pages 853-881, May.
    6. Kurosaki, Tetsuo & Kim, Young Shin, 2022. "Cryptocurrency portfolio optimization with multivariate normal tempered stable processes and Foster-Hart risk," Finance Research Letters, Elsevier, vol. 45(C).
    7. Young Shin Kim, 2020. "Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk," Papers 2007.13972, arXiv.org, revised Sep 2020.
    8. Young Shin Kim, 2019. "Tempered stable process, first passage time, and path-dependent option pricing," Computational Management Science, Springer, vol. 16(1), pages 187-215, February.
    9. Tetsuo Kurosaki & Young Shin Kim, 2020. "Cryptocurrency portfolio optimization with multivariate normal tempered stable processes and Foster-Hart risk," Papers 2010.08900, arXiv.org.
    10. Young Shin Kim & Frank J. Fabozzi, 2024. "Portfolio optimization with relative tail risk," Annals of Operations Research, Springer, vol. 341(2), pages 1023-1055, October.
    11. Holger Fink & Stefan Mittnik, 2021. "Quanto Pricing beyond Black–Scholes," JRFM, MDPI, vol. 14(3), pages 1-27, March.
    12. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    13. Kim, Sung Ik, 2023. "A comparative study of firm value models: Default risk of corporate bonds," Finance Research Letters, Elsevier, vol. 56(C).
    14. Tiantian Li & Young Shin Kim & Qi Fan & Fumin Zhu, 2021. "Aumann–Serrano index of risk in portfolio optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 197-217, October.
    15. Battauz, Anna & De Donno, Marzia & Sbuelz, Alessandro, 2022. "On the exercise of American quanto options," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    16. Chang, C-L. & McAleer, M.J., 2014. "Econometric Analysis of Financial Derivatives," Econometric Institute Research Papers EI 2015-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Sung Ik Kim & Young Shin Kim, 2018. "Tempered stable structural model in pricing credit spread and credit default swap," Review of Derivatives Research, Springer, vol. 21(1), pages 119-148, April.
    18. Young Shin Kim & Hyun-Gyoon Kim, 2024. "Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence," Papers 2402.17919, arXiv.org, revised Mar 2024.
    19. Hasan A. Fallahgoul & Young S. Kim & Frank J. Fabozzi & Jiho Park, 2019. "Quanto Option Pricing with Lévy Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1279-1308, March.
    20. Lisha Lin & Yaqiong Li & Rui Gao & Jianhong Wu, 2019. "The Numerical Simulation of Quanto Option Prices Using Bayesian Statistical Methods," Papers 1910.04075, arXiv.org.
    21. Young Shin Kim, 2023. "Portfolio Optimization with Relative Tail Risk," Papers 2303.12209, arXiv.org, revised Mar 2023.
    22. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.

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