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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.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 17/02.

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Length: 42 pages
Date of creation: Nov 2002
Date of revision:
Handle: RePEc:msh:ebswps:2002-17

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Keywords: Box-Cox transformations; Stochastic volatility; MCMC; Exchange rate volatility; Option pricing.;

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Cited by:
  1. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. 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.
  3. 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.
  4. Xibin Zhang & Maxwell L. King, 2004. "Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors," Monash Econometrics and Business Statistics Working Papers 26/04, Monash University, Department of Econometrics and Business Statistics.
  5. Weigand, Roland, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," University of Regensburg Working Papers in Business, Economics and Management Information Systems 478, University of Regensburg, Department of Economics.
  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. Esther Ruiz & Helena Veiga, 2006. "Modelling Long-Memory Volatilities With Leverage Effect: Almsv Versus Fiegarch," Statistics and Econometrics Working Papers ws066016, Universidad Carlos III, Departamento de Estadística y Econometría.
  8. Jun Yu, 2010. "Simulation-based Estimation Methods for Financial Time Series Models," Working Papers 19-2010, Singapore Management University, School of Economics.
  9. Daniel Preve & Anders Eriksson & Jun Yu, 2009. "Forecasting Realized Volatility Using A Nonnegative Semiparametric Model," Finance Working Papers 23049, East Asian Bureau of Economic Research.
  10. 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.
  11. 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.
  12. Borovkova, Svetlana & Permana, Ferry J., 2009. "Implied volatility in oil markets," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2022-2039, April.
  13. Georgios Tsiotas, 2009. "On the use of non-linear transformations in Stochastic Volatility models," Statistical Methods and Applications, Springer, vol. 18(4), pages 555-583, November.
  14. 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.

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