Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model

Published Online:https://doi.org/10.1287/opre.2017.1636

References

  • Abate J, Whitt W (1992) The Fourier-series method for inverting transforms of probability distributions. Queueing Systems Theory Appl. 10(1–2):5–87.CrossrefGoogle Scholar
  • Ahdida A, Alfonsi A (2013) Exact and high order discretization schemes for Wishart processes and their affine extensions. Ann. Appl. Probab. 23(3):1025–1073.CrossrefGoogle Scholar
  • Amos DE (1986) Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order. ACM Trans. Math. Software 12(3, Sept.):265–273.Google Scholar
  • Bates D (1996) Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Rev. Financ. Stud. 9(1):69–107.CrossrefGoogle Scholar
  • Bates DS (2000) Post-’87 crash fears in the S&P 500 futures option market. J. Econometrics 94(1–2):181–238.CrossrefGoogle Scholar
  • Benabid A, Bensusan H, El Karoui N,et al. (2008) Wishart stochastic volatility: Asymptotic smile and numerical framework. Preprint.Google Scholar
  • Broadie M, Kaya Ö (2006) Exact simulation of stochastic volatility and other affine jump diffusion processes. Oper. Res. 54(2):217–231.LinkGoogle Scholar
  • Bru M-F (1991) Wishart processes. J. Theoret. Probab. 4(4):725–751.CrossrefGoogle Scholar
  • Carr P, Wu L (2007) Stochastic skew in currency options. J. Financial Econom. 86(1):213–247.CrossrefGoogle Scholar
  • Carr P, Madan DB, Smith RH (1999) Option valuation using the fast Fourier transform. J. Computational Finance 2(4):61–73.CrossrefGoogle Scholar
  • Christoffersen P, Heston S, Jacobs K (2009) The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well. Management Sci. 55(12):1914–1932.LinkGoogle Scholar
  • Cuchiero C, Filipović D, Mayerhofer E, Teichmann J (2011) Affine processes on positive semidefinite matrices. Ann. Appl. Probab. 21(2):397–463.CrossrefGoogle Scholar
  • da Fonseca J, Grasselli M (2011) Riding on the smiles. Quant. Finance 11(11):1609–1632.CrossrefGoogle Scholar
  • da Fonseca J, Grasselli M, Tebaldi C (2008) A multifactor volatility Heston model. Quant. Finance 8(6):591–604.CrossrefGoogle Scholar
  • Dormand JR, Prince PJ (1980) A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6(1):19–26.CrossrefGoogle Scholar
  • Duffie D, Pan J, Singleton K (2000) Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68(6):1343–1376.CrossrefGoogle Scholar
  • Durrett R (2010) Probability: Theory and Examples (Cambridge University Press, New York).CrossrefGoogle Scholar
  • Filipović D (2009) Term-Structure Models, Springer Finance (Springer, Berlin).CrossrefGoogle Scholar
  • Gauthier P, Possamaï D (2011) Prices expansion in the Wishart model. The IUP J. Computational Math. 4(1):44–71.Google Scholar
  • Gauthier P, Possamaï D (2012) Efficient simulation of the Wishart model. The IUP J. Computational Math. 5(1):14–58.Google Scholar
  • Glasserman P (2004) Monte Carlo Methods in Financial Engineering, Volume 53 of Applications of Mathematics (New York), Stochastic Modelling and Applied Probability (Springer, New York).Google Scholar
  • Gleser LJ (1976) A canonical representation for the noncentral Wishart distribution useful for simulation. J. Amer. Statist. Assoc. 71(355):690–695.CrossrefGoogle Scholar
  • Gourieroux C, Sufana R (2010) Derivative pricing with Wishart multivariate stochastic volatility. J. Bus. Econom. Statist. 28(3):438–451.CrossrefGoogle Scholar
  • Gupta AK, Nagar DK (2000) Matrix Variate Distributions, Volume 104 of Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics (Chapman & Hall/CRC, Boca Raton, FL).Google Scholar
  • Heston S (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. 6(2):327–343.CrossrefGoogle Scholar
  • Kang C, Kang W (2013) Transform formulae for linear functionals of affine processes and their bridges on positive semidefinite matrices. Stochastic Process. Appl. 123(6):2419–2445.CrossrefGoogle Scholar
  • Koev P, Edelman A (2006) The efficient evaluation of the hypergeometric function of a matrix argument. Math. Comp. 75(254):833–846.CrossrefGoogle Scholar
  • Kshirsagar AM (1959) Bartlett decomposition and Wishart distribution. Ann. Math. Statist. 30(1):239–241.CrossrefGoogle Scholar
  • Leippold M, Trojani F (2008) Asset pricing with matrix jump diffusions. Preprint.Google Scholar
  • Muirhead RJ (1982) Aspects of Multivariate Statistical Theory, Wiley Series in Probability and Mathematical Statistics (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • Van Haastrecht A, Pelsser A (2010) Efficient, almost exact simulation of the Heston stochastic volatility model. Internat. J. Theoret. Appl. Finance 13(01):1–43.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.