메뉴 건너뛰기




Volumn 30, Issue 3, 2002, Pages 754-783

Asymptotic nonequivalence of GARCH models and diffusions

Author keywords

ARCH; Black Scholes; Comparison of experiments; Conditional variance; Deficiency distance; Financial modeling; Likelihood process; Stochastic differential equation; Stochastic volatility

Indexed keywords


EID: 0036051612     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1028674841     Document Type: Article
Times cited : (89)

References (49)
  • 1
    • 0030369366 scopus 로고    scopus 로고
    • Nonparametric pricing of interest rate derivative securities
    • AÏT-SAHALIA, Y. (1996). Nonparametric pricing of interest rate derivative securities. Econometrica 64 527-560.
    • (1996) Econometrica , vol.64 , pp. 527-560
    • Aït-Sahalia, Y.1
  • 3
    • 85015692260 scopus 로고
    • The pricing of options and corporate liabilities
    • BLACK, F. and SCHOLES, M. (1973). The pricing of options and corporate liabilities. J. Political Economy 81 637-659.
    • (1973) J. Political Economy , vol.81 , pp. 637-659
    • Black, F.1    Scholes, M.2
  • 4
    • 42449156579 scopus 로고
    • Generalized autoregressive conditional heteroskedasticity
    • BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31 307-327.
    • (1986) J. Econometrics , vol.31 , pp. 307-327
    • Bollerslev, T.1
  • 5
    • 34848900983 scopus 로고
    • ARCH modeling in finance. A review of the theory and empirical evidence
    • BOLLERSLEV, T., CHOU, R. Y. and KRONER, K. F. (1992). ARCH modeling in finance. A review of the theory and empirical evidence. J. Econometrics 52 5-59.
    • (1992) J. Econometrics , vol.52 , pp. 5-59
    • Bollerslev, T.1    Chou, R.Y.2    Kroner, K.F.3
  • 6
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • BROWN, L. and LOW, M. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398.
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.1    Low, M.2
  • 8
    • 43949160158 scopus 로고
    • Stochastic volatility in asset prices: Estimation with simulated maximum likelihood
    • DANIELSSON, J. (1994). Stochastic volatility in asset prices: Estimation with simulated maximum likelihood. J. Econometrics 64 375-400.
    • (1994) J. Econometrics , vol.64 , pp. 375-400
    • Danielsson, J.1
  • 10
    • 0000446476 scopus 로고    scopus 로고
    • Efficient estimation in semiparametric GARCH models
    • DROST, F. C. and KLAASSEN, C. A. J. (1997). Efficient estimation in semiparametric GARCH models. J. Econometrics 81 193-221.
    • (1997) J. Econometrics , vol.81 , pp. 193-221
    • Drost, F.C.1    Klaassen, C.A.J.2
  • 11
    • 0002567184 scopus 로고
    • The GARCH option pricing model
    • DUAN, J. C. (1995). The GARCH option pricing model. Math. Finance 5 13-32.
    • (1995) Math. Finance , vol.5 , pp. 13-32
    • Duan, J.C.1
  • 12
    • 0002229006 scopus 로고    scopus 로고
    • Augmented GARCH(p, q) process and its diffusion limit
    • DUAN, J. C. (1997). Augmented GARCH(p, q) process and its diffusion limit. J. Econometrics 79 97-127.
    • (1997) J. Econometrics , vol.79 , pp. 97-127
    • Duan, J.C.1
  • 14
    • 0000051984 scopus 로고
    • Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
    • ENGLE, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 987-1007.
    • (1982) Econometrica , vol.50 , pp. 987-1007
    • Engle, R.F.1
  • 15
    • 84963146757 scopus 로고
    • Modeling the persistence of conditional variances
    • ENGLE, R. F. and BOLLERSLEV, T. (1986). Modeling the persistence of conditional variances (with discussion). Econometric Rev. 5 1-87.
    • (1986) Econometric Rev. , vol.5 , pp. 1-87
    • Engle, R.F.1    Bollerslev, T.2
  • 16
    • 84881079791 scopus 로고
    • Approximate discrete time schemes for statistics of diffusion processes
    • FLORENS-ZMIROU, D. (1989). Approximate discrete time schemes for statistics of diffusion processes. Statistics 20 547-557.
    • (1989) Statistics , vol.20 , pp. 547-557
    • Florens-Zmirou, D.1
  • 17
    • 0000890084 scopus 로고    scopus 로고
    • Estimation of stochastic volatility models with diagnostics
    • GALLANT, A. R., HSIEH, D., and TAUCHEN, G. (1997). Estimation of stochastic volatility models with diagnostics. J. Econometrics 81 159-192.
    • (1997) J. Econometrics , vol.81 , pp. 159-192
    • Gallant, A.R.1    Hsieh, D.2    Tauchen, G.3
  • 18
    • 33746404294 scopus 로고    scopus 로고
    • Estimating stochastic differential equations efficiently by minimum chi-squared
    • GALLANT, A. R. and LONG, J. R. (1997). Estimating stochastic differential equations efficiently by minimum chi-squared. Biometrika 84 125-141.
    • (1997) Biometrika , vol.84 , pp. 125-141
    • Gallant, A.R.1    Long, J.R.2
  • 19
    • 0032346647 scopus 로고    scopus 로고
    • Reprojecting partially observed systems with application to interest rate diffusions
    • GALLANT, A. R. and TAUCHEN, G. (1998). Reprojecting partially observed systems with application to interest rate diffusions. J. Amer. Statist. Assoc. 93 10-24.
    • (1998) J. Amer. Statist. Assoc. , vol.93 , pp. 10-24
    • Gallant, A.R.1    Tauchen, G.2
  • 20
    • 0002074626 scopus 로고
    • Maximum contrast estimation for diffusion processes from discrete observations
    • GENON-CATALOT, V. (1990). Maximum contrast estimation for diffusion processes from discrete observations. Statistics 21 99-116.
    • (1990) Statistics , vol.21 , pp. 99-116
    • Genon-Catalot, V.1
  • 21
    • 84963255699 scopus 로고
    • Modeling the persistence of conditional variances
    • by R. F. Engle and T. Bollerslev
    • GEWEKE, J. (1986). Comment on "Modeling the persistence of conditional variances," by R. F. Engle and T. Bollerslev. Econometric Rev. 5 57-61.
    • (1986) Econometric Rev. , vol.5 , pp. 57-61
    • Geweke, J.1
  • 23
    • 38649141305 scopus 로고
    • Martingales and arbitrage in multiperiod securities markets
    • HARRISON, J. M. and KREPS, D. (1979). Martingales and arbitrage in multiperiod securities markets. J. Econom. Theory 20 381-408.
    • (1979) J. Econom. Theory , vol.20 , pp. 381-408
    • Harrison, J.M.1    Kreps, D.2
  • 24
    • 41649091143 scopus 로고
    • Martingales and stochastic integrals in the theory of continuous trading
    • HARRISON, J. M. and PLISKA, S. (1981). Martingales and stochastic integrals in the theory of continuous trading. Stochastic Process. Appl. 11 215-260.
    • (1981) Stochastic Process. Appl. , vol.11 , pp. 215-260
    • Harrison, J.M.1    Pliska, S.2
  • 25
    • 84977719043 scopus 로고
    • Chaos and nonlinear dynamics: Application to financial markets
    • HSIEH, D. (1991). Chaos and nonlinear dynamics: Application to financial markets. J. Finance 46 1839-1877.
    • (1991) J. Finance , vol.46 , pp. 1839-1877
    • Hsieh, D.1
  • 27
    • 84977709229 scopus 로고
    • The pricing of options on assets with stochastic volatilities
    • HULL, J. and WHITE, A. (1987). The pricing of options on assets with stochastic volatilities. J. Finance 42 281-300.
    • (1987) J. Finance , vol.42 , pp. 281-300
    • Hull, J.1    White, A.2
  • 31
    • 84952181953 scopus 로고
    • Bayesian analysis of stochastic volatility models
    • JACQUIER, E., POLSON, N. G. and ROSSI, P. E. (1994). Bayesian analysis of stochastic volatility models (with discussion). J. Bus. Econom. Statist. 12 371-417.
    • (1994) J. Bus. Econom. Statist. , vol.12 , pp. 371-417
    • Jacquier, E.1    Polson, N.G.2    Rossi, P.E.3
  • 33
    • 0040360923 scopus 로고    scopus 로고
    • Estimation of an ergodic diffusion from discrete observations
    • KESSLER, M. (1997). Estimation of an ergodic diffusion from discrete observations. Scand, J. Statist. 24 211-229.
    • (1997) Scand, J. Statist. , vol.24 , pp. 211-229
    • Kessler, M.1
  • 34
    • 0000411204 scopus 로고
    • An approximation of partial sums of independent RVs and the sample DF
    • KOMLÓS, J., MAJOR, P. and TUSNÁDY, G. (1975). An approximation of partial sums of independent RVs and the sample DF. I. Z. Wahrsch. Verw. Gebiete 32 111-131.
    • (1975) I. Z. Wahrsch. Verw. Gebiete , vol.32 , pp. 111-131
    • Komlós, J.1    Major, P.2    Tusnády, G.3
  • 37
    • 0015602539 scopus 로고
    • The theory of rational option pricing
    • MERTON, R. (1973). The theory of rational option pricing. Bell J. Econom. Management Sci. 4 141-183.
    • (1973) Bell J. Econom. Management Sci. , vol.4 , pp. 141-183
    • Merton, R.1
  • 39
    • 0043114353 scopus 로고    scopus 로고
    • Options pricing in incomplete markets: An asymptotic approach
    • Dept. Statist., Univ. Chicago
    • MYKLAND, P. A. (1996). Options pricing in incomplete markets: an asymptotic approach. Technical Report 430, Dept. Statist., Univ. Chicago.
    • (1996) Technical Report , vol.430
    • Mykland, P.A.1
  • 40
    • 0842316847 scopus 로고
    • ARCH models as diffusion approximations
    • NELSON, D. B. (1990). ARCH models as diffusion approximations. J. Econometrics 45 7-38.
    • (1990) J. Econometrics , vol.45 , pp. 7-38
    • Nelson, D.B.1
  • 41
    • 44049123033 scopus 로고
    • Filtering and forecasting with misspecified ARCH models I. Getting the right variance with the wrong model
    • NELSON, D. B. (1992). Filtering and forecasting with misspecified ARCH models I. Getting the right variance with the wrong model. J. Econometrics 52 61-90.
    • (1992) J. Econometrics , vol.52 , pp. 61-90
    • Nelson, D.B.1
  • 42
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • NUSSBAUM, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430.
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 43
    • 84963255679 scopus 로고
    • Modeling the persistence of conditional variances
    • by R. F. Engle and T. Bollerslev
    • PANTULA, S. G. (1986). Comment on "Modeling the persistence of conditional variances," by R. F. Engle and T. Bollerslev. Econometric Rev. 5 71-74.
    • (1986) Econometric Rev. , vol.5 , pp. 71-74
    • Pantula, S.G.1
  • 44
    • 0006599335 scopus 로고
    • Statistical inference from sampled data for stochastic processes
    • N. U. Prabha, ed. Amer. Math. Soc., Providence, RI
    • PRAKASA RAO, B. L. S. (1988). Statistical inference from sampled data for stochastic processes. In Statistical Inference from Stochastic Processes (N. U. Prabha, ed.) 249-284. Amer. Math. Soc., Providence, RI.
    • (1988) Statistical Inference from Stochastic Processes , pp. 249-284
    • Prakasa Rao, B.L.S.1
  • 48
    • 0001866651 scopus 로고
    • A remark on the approximation of the sample distribution function in the multidimensional case
    • TUSNÁDY, G. (1977). A remark on the approximation of the sample distribution function in the multidimensional case. Period. Math. Hungar. 8 53-55.
    • (1977) Period. Math. Hungar. , vol.8 , pp. 53-55
    • Tusnády, G.1
  • 49
    • 0000574485 scopus 로고
    • Estimation for diffusion processes from discrete observations
    • YOSHIDA, N. (1992). Estimation for diffusion processes from discrete observations. J. Multivariate Anal. 41 220-242.
    • (1992) J. Multivariate Anal. , vol.41 , pp. 220-242
    • Yoshida, N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.