×

zbMATH — the first resource for mathematics

Modeling stochastic volatility: A review and comparative study. (English) Zbl 0884.90054
Summary: Diffusion models for volatility have been used to price options while ARCH models predominate in descriptive studies of asset volatility. This paper compares a discrete-time approximation of a popular diffusion model with ARCH models. These volatility models have many similarities but the models make different assumptions about how the magnitude of price responses to information alters volatility and the amount of subsequent information. Several volatility models are estimated for daily DM/$ exchange rates from 1978 to 1990.

MSC:
91B28 Finance etc. (MSC2000)
91B84 Economic time series analysis
91B62 Economic growth models
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1086/296451 · doi:10.1086/296451
[2] Andersen T. G., Volatility (1992)
[3] Andersen T. G., Return Volatility and Trading Volume: an Information Flow Interpretation of Stochastic Volatility (1993)
[4] DOI: 10.2307/2330744 · doi:10.2307/2330744
[5] DOI: 10.2307/1391527 · doi:10.2307/1391527
[6] DOI: 10.1007/BF00114078 · doi:10.1007/BF00114078
[7] DOI: 10.2307/2330824 · doi:10.2307/2330824
[8] DOI: 10.1016/0304-4076(86)90063-1 · Zbl 0616.62119 · doi:10.1016/0304-4076(86)90063-1
[9] DOI: 10.2307/1925546 · doi:10.2307/1925546
[10] DOI: 10.1016/0304-4076(92)90064-X · Zbl 0825.90057 · doi:10.1016/0304-4076(92)90064-X
[11] Bollerslev T, The Handbook of Econometrics 4 (1993)
[12] Bollerslev T., Econometric Rev. 11 pp 143– (1992)
[13] Box G. E. P., Bayesian Inference in Statistical Analysis. (1973) · Zbl 0271.62044
[14] DOI: 10.2307/2328994 · doi:10.2307/2328994
[15] DOI: 10.1016/0304-405X(92)90037-X · doi:10.1016/0304-405X(92)90037-X
[16] DOI: 10.2307/2330812 · doi:10.2307/2330812
[17] DOI: 10.2307/1913889 · Zbl 0308.90011 · doi:10.2307/1913889
[18] DOI: 10.1016/0304-4076(92)90073-Z · Zbl 04506591 · doi:10.1016/0304-4076(92)90073-Z
[19] Duan J.-C., Math. Finance 4 (2) (1993)
[20] DUFFIE D., Simulated Moments Estimation of Markov Models of Asset Prices (1989) · Zbl 0783.62099
[21] DOI: 10.2307/1912773 · Zbl 0491.62099 · doi:10.2307/1912773
[22] Engle R. F., Econometric Rev. 5 pp 1– (1986)
[23] DOI: 10.2307/1391236 · doi:10.2307/1391236
[24] DOI: 10.1016/0304-4076(92)90074-2 · Zbl 04506593 · doi:10.1016/0304-4076(92)90074-2
[25] DOI: 10.1016/0304-405X(86)90004-8 · doi:10.1016/0304-405X(86)90004-8
[26] Gallant A. R., Nonparametric and Semiparametric Methods in Econometrics and Statistics (1991)
[27] DOI: 10.2307/2330708 · doi:10.2307/2330708
[28] Harvey A. C., Rev. Economic Stud. (1994)
[29] Harvey A. C., The Econometrics of Stochastic Volatility (1993)
[30] DOI: 10.1093/rfs/6.2.327 · Zbl 1384.35131 · doi:10.1093/rfs/6.2.327
[31] DOI: 10.2307/1391528 · doi:10.2307/1391528
[32] Hsu D.-A., J. Navigation 33 pp 452– (1980)
[33] DOI: 10.2307/2287766 · doi:10.2307/2287766
[34] DOI: 10.2307/2328253 · doi:10.2307/2328253
[35] DOI: 10.1016/0261-5606(87)90029-5 · doi:10.1016/0261-5606(87)90029-5
[36] Hull J., Adv. Futures Options Res. 3 pp 29– (1988)
[37] Jacquier E., J. Business Econ. Statis. (1994)
[38] DOI: 10.2307/2330709 · doi:10.2307/2330709
[39] Kelly F. P., Reversibility and Stochastic Networks. (1979)
[40] DOI: 10.2307/2328817 · doi:10.2307/2328817
[41] DOI: 10.2307/1992578 · doi:10.2307/1992578
[42] Lumsdaine R. L., Asymptotic Properties of the Quasi-Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models (1991) · Zbl 0844.62080
[43] Lumsdaine R. L., Finite Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation (1991)
[44] DOI: 10.2307/2327703 · doi:10.2307/2327703
[45] DOI: 10.1016/0304-4076(90)90100-8 · Zbl 04574635 · doi:10.1016/0304-4076(90)90100-8
[46] DOI: 10.1016/0304-405X(89)90078-0 · doi:10.1016/0304-405X(89)90078-0
[47] DOI: 10.1016/0304-4076(90)90092-8 · Zbl 0719.60089 · doi:10.1016/0304-4076(90)90092-8
[48] DOI: 10.2307/2938260 · Zbl 0722.62069 · doi:10.2307/2938260
[49] DOI: 10.1086/295425 · doi:10.1086/295425
[50] DOI: 10.2307/2328718 · doi:10.2307/2328718
[51] DOI: 10.2307/2330793 · doi:10.2307/2330793
[52] Scott L. O., Adv. Futures Options Res. 5 pp 113– (1991)
[53] Scott L. O., Stock Market Volatility and the Pricing of Index Options: an Analysis of Implied Volatilities and the Volatility Risk Premium in a Model with Stochastic Interest Rates and Volatility (1992)
[54] DOI: 10.1093/rfs/4.4.727 · Zbl 1458.62253 · doi:10.1093/rfs/4.4.727
[55] DOI: 10.2307/2328621 · doi:10.2307/2328621
[56] DOI: 10.2307/1912002 · Zbl 0495.90026 · doi:10.2307/1912002
[57] Taylor S. J., Modelling Financial Time Series. (1986) · Zbl 1130.91345
[58] DOI: 10.1016/0304-405X(87)90009-2 · doi:10.1016/0304-405X(87)90009-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.