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Simulation methods for Lévy-driven continuous-time autoregressive moving average (CARMA) stochastic volatility models

Publication ,  Journal Article
Todorov, V; Tauchen, G
Published in: Journal of Business and Economic Statistics
October 1, 2006

We develop simulation schemes for the new classes of non-Gaussian pure jump Lévy processes for stochastic volatility. We write the price and volatility processes as integrals against a vector Lévy process, which makes series approximation methods directly applicable. These methods entail simulation of the Lévy increments and formation of weighted sums of the increments; they do not require a closed-form expression for a tail mass function or specification of a copula function. We also present a new, and apparently quite flexible, bivariate mixture-of-gammas model for the driving Lévy process. Within this setup, it is quite straightforward to generate simulations from a Lévy-driven continuous-time autoregressive moving average stochastic volatility model augmented by a pure-jump price component. Simulations reveal the wide range of different types of financial price processes that can be generated in this manner, including processes with persistent stochastic volatility, dynamic leverage, and jumps. © 2006 American Statistical Association Journal of Business & Economic Statistics.

Duke Scholars

Published In

Journal of Business and Economic Statistics

DOI

ISSN

0735-0015

Publication Date

October 1, 2006

Volume

24

Issue

4

Start / End Page

455 / 469

Related Subject Headings

  • Econometrics
  • 49 Mathematical sciences
  • 38 Economics
  • 35 Commerce, management, tourism and services
  • 15 Commerce, Management, Tourism and Services
  • 14 Economics
  • 01 Mathematical Sciences
 

Citation

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Todorov, V., & Tauchen, G. (2006). Simulation methods for Lévy-driven continuous-time autoregressive moving average (CARMA) stochastic volatility models. Journal of Business and Economic Statistics, 24(4), 455–469. https://doi.org/10.1198/073500106000000260
Todorov, V., and G. Tauchen. “Simulation methods for Lévy-driven continuous-time autoregressive moving average (CARMA) stochastic volatility models.” Journal of Business and Economic Statistics 24, no. 4 (October 1, 2006): 455–69. https://doi.org/10.1198/073500106000000260.
Todorov V, Tauchen G. Simulation methods for Lévy-driven continuous-time autoregressive moving average (CARMA) stochastic volatility models. Journal of Business and Economic Statistics. 2006 Oct 1;24(4):455–69.
Todorov, V., and G. Tauchen. “Simulation methods for Lévy-driven continuous-time autoregressive moving average (CARMA) stochastic volatility models.” Journal of Business and Economic Statistics, vol. 24, no. 4, Oct. 2006, pp. 455–69. Scopus, doi:10.1198/073500106000000260.
Todorov V, Tauchen G. Simulation methods for Lévy-driven continuous-time autoregressive moving average (CARMA) stochastic volatility models. Journal of Business and Economic Statistics. 2006 Oct 1;24(4):455–469.
Journal cover image

Published In

Journal of Business and Economic Statistics

DOI

ISSN

0735-0015

Publication Date

October 1, 2006

Volume

24

Issue

4

Start / End Page

455 / 469

Related Subject Headings

  • Econometrics
  • 49 Mathematical sciences
  • 38 Economics
  • 35 Commerce, management, tourism and services
  • 15 Commerce, Management, Tourism and Services
  • 14 Economics
  • 01 Mathematical Sciences