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A Class of Nonlinear Stochastic Volatility Models and Its Implications on Pricing Currency Options

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  • Jun Yu
  • Zhenlin Yang
  • Xibin Zhang

Abstract

This paper proposes a class of stochastic volatility (SV) models which offers an alternative to the one introduced in Andersen (1994). The class encompasses all standard SV models that have appeared in the literature, including the well known lognormal model, and allows us to empirically test all standard specifications in a convenient way. We develop a likelihood-based technique for analyzing the class. Daily dollar/pound exchange rate data reject all the standard models and suggest evidence of nonlinear SV. An efficient algorithm is proposed to study the implications of this nonlinear SV on pricing currency options and it is found that the lognormal model overprices options.

Suggested Citation

  • Jun Yu & Zhenlin Yang & Xibin Zhang, 2002. "A Class of Nonlinear Stochastic Volatility Models and Its Implications on Pricing Currency Options," Monash Econometrics and Business Statistics Working Papers 17/02, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2002-17
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    3. Isabel Casas & Helena Veiga, 2021. "Exploring Option Pricing and Hedging via Volatility Asymmetry," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1015-1039, April.
    4. Jun Yu, 2010. "Simulation-based Estimation Methods for Financial Time Series Models," Working Papers 19-2010, Singapore Management University, School of Economics.
    5. Goodwin, Roger L, 2015. "Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.3," MPRA Paper 64863, University Library of Munich, Germany, revised 07 Jun 2015.
    6. Kotchoni, Rachidi, 2012. "Applications of the characteristic function-based continuum GMM in finance," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3599-3622.
    7. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    8. Zhongxian Men & Adam W. Kolkiewicz & Tony S. Wirjanto, 2019. "Threshold Stochastic Conditional Duration Model for Financial Transaction Data," JRFM, MDPI, vol. 12(2), pages 1-21, May.
    9. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
    10. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xi-Li & Wang, Ying-Luo, 2010. "Pricing currency options in a fractional Brownian motion with jumps," Economic Modelling, Elsevier, vol. 27(5), pages 935-942, September.
    11. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    12. Mao, Xiuping & Ruiz, Esther & Veiga, Helena, 2017. "Threshold stochastic volatility: Properties and forecasting," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1105-1123.
    13. Goodwin, Roger L, 2014. "Random Variables, Their Properties, and Deviational Ellipses: In Map Point and Excel, v 4.0," MPRA Paper 64101, University Library of Munich, Germany, revised 17 Apr 2015.
    14. Zhongxian Men & Tony S. Wirjanto & Adam W. Kolkiewicz, 2021. "Multiscale Stochastic Volatility Model with Heavy Tails and Leverage Effects," JRFM, MDPI, vol. 14(5), pages 1-28, May.
    15. Foschi, Paolo & Pascucci, Andrea, 2009. "Calibration of a path-dependent volatility model: Empirical tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2219-2235, April.
    16. Georgios Tsiotas, 2009. "On the use of non-linear transformations in Stochastic Volatility models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 555-583, November.
    17. Mao, Xiuping & Ruiz Ortega, Esther & Lopes Moreira Da Veiga, María Helena, 2013. "One for all : nesting asymmetric stochastic volatility models," DES - Working Papers. Statistics and Econometrics. WS ws131110, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Kawakatsu, Hiroyuki, 2007. "Specification and estimation of discrete time quadratic stochastic volatility models," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 424-442, June.
    19. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    20. Ruiz, Esther & Veiga, Helena, 2008. "Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2846-2862, February.
    21. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    22. Borovkova, Svetlana & Permana, Ferry J., 2009. "Implied volatility in oil markets," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2022-2039, April.
    23. Didit Budi Nugroho & Takayuki Morimoto, 2019. "Incorporating Realized Quarticity into a Realized Stochastic Volatility Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(4), pages 495-528, December.
    24. Giannikis, D. & Vrontos, I.D. & Dellaportas, P., 2008. "Modelling nonlinearities and heavy tails via threshold normal mixture GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1549-1571, January.
    25. Georgios Tsiotas, 2020. "On the use of power transformations in CAViaR models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 296-312, March.

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    More about this item

    Keywords

    Box-Cox transformations; Stochastic volatility; MCMC; Exchange rate volatility; Option pricing.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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