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Pricing short-dated foreign equity options with a bivariate jump-diffusion model with correlated fat-tailed jumps

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  • Ulyah, Siti Maghfirotul
  • Lin, Xenos Chang-Shuo
  • Miao, Daniel Wei-Chung

Abstract

This paper considers short-dated foreign equity options (FEOs) and proposes a new model for their pricing. When time to maturity is short, the possibility of seeing jumps caused by a forthcoming big event will make the return distributions of both assets (equity and exchange rate) very fat-tailed, resulting in a much higher kurtosis compared to longer time to maturity. The impact is even stronger when the jumps from the two assets are highly and positively correlated so that their effects will add up. In the proposed BB-BAL jump-diffusion model, we use a bivariate Bernoulli (BB) distribution to model the jump indicators of the two assets. The jump sizes of two assets are assumed to follow a bivariate asymmetric Laplace (BAL) distribution which captures their tail-fatness as well as their potentially strong correlation simultaneously. We provide an analysis for the proposed model and derives the analytical results for FEO prices. Through numerical examples we show that the jump correlation may lead to very high kurtosis and have a significant impact on the short-dated FEO prices.

Suggested Citation

  • Ulyah, Siti Maghfirotul & Lin, Xenos Chang-Shuo & Miao, Daniel Wei-Chung, 2018. "Pricing short-dated foreign equity options with a bivariate jump-diffusion model with correlated fat-tailed jumps," Finance Research Letters, Elsevier, vol. 24(C), pages 113-128.
  • Handle: RePEc:eee:finlet:v:24:y:2018:i:c:p:113-128
    DOI: 10.1016/j.frl.2017.07.012
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    1. Fernanda D'Ippoliti & Enrico Moretto & Sara Pasquali & Barbara Trivellato, 2010. "Exact Pricing With Stochastic Volatility And Jumps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 901-929.
    2. Jondeau, Eric & Rockinger, Michael, 2001. "Gram-Charlier densities," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1457-1483, October.
    3. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    4. Yue-Kuen Kwok & Hoi-Ying Wong, 2000. "Currency-Translated Foreign Equity Options With Path Dependent Features And Their Multi-Asset Extensions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 257-278.
    5. Shian‐Chang Huang & Mao‐Wei Hung, 2005. "Pricing foreign equity options under Lévy processes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(10), pages 917-944, October.
    6. Gerald Cheang & Carl Chiarella, 2011. "A Modern View on Merton's Jump-Diffusion Model," Research Paper Series 287, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 211-239, June.
    8. 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.
    9. Pierre Bajgrowicz & Olivier Scaillet & Adrien Treccani, 2016. "Jumps in High-Frequency Data: Spurious Detections, Dynamics, and News," Management Science, INFORMS, vol. 62(8), pages 2198-2217, August.
    10. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    11. Wei, J.Z. & Duan, J.C., 1999. "Pricing Foreign Currency and Cross-Currency Options Under GARCH," Rotman School of Management - Finance 99-01, Rotman School of Management, University of Toronto.
    12. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Foreign equity option pricing under stochastic volatility model with double jumps," Economic Modelling, Elsevier, vol. 28(4), pages 1857-1863, July.
    13. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Accounting for the impact of higher order moments in foreign equity option pricing model," Economic Modelling, Elsevier, vol. 28(4), pages 1726-1729, July.
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