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Stochastic Volatility: Origins and Overview

  • Neil Shephard
  • Torben G. Andersen

In this paper we review the history and recent developments of stochastic volatility, which is the main way financial economists and mathematical finance specialists model time varying volatility.

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Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2008fe23.

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Length: 21
Date of creation: 2008
Date of revision:
Handle: RePEc:sbs:wpsefe:2008fe23
Contact details of provider: Web page: http://www.finance.ox.ac.uk
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  1. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
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  6. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
  7. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
  8. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  9. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
  10. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2007. "Real-time price discovery in global stock, bond and foreign exchange markets," Journal of International Economics, Elsevier, vol. 73(2), pages 251-277, November.
  11. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
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  13. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2003. "Likelihood-Based Estimation Of Latent Generalised Arch Structures," Working Papers. Serie AD 2003-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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  15. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
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  17. Marc Yor & Dilip B. Madan & Hélyette Geman, 2002. "Stochastic volatility, jumps and hidden time changes," Finance and Stochastics, Springer, vol. 6(1), pages 63-90.
  18. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  19. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  20. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  21. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2005. "Real-Time Price Discovery in Stock, Bond and Foreign Exchange Markets," NBER Working Papers 11312, National Bureau of Economic Research, Inc.
  22. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January.
  23. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201, March.
  24. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers 95-36, Duke University, Department of Economics.
  25. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
  26. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
  27. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
  28. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
  29. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  30. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  31. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  32. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
  33. Liesenfeld, Roman, 2001. "A generalized bivariate mixture model for stock price volatility and trading volume," Journal of Econometrics, Elsevier, vol. 104(1), pages 141-178, August.
  34. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.
  35. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.
  36. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
  37. Back, Kerry, 1991. "Asset pricing for general processes," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 371-395.
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