Parameter estimation for discretely observed stochastic volatility models

Bernoulli

Volumn 5, Issue 5, 1999, Pages 855-872

  Genon Catalot, Valentine ^a,b   Jeantheau, Thierry ^a,b   Laredo, Catherine ^a,b  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b CEMAGREF   (France)

Author keywords

Diffusion processes; Discrete time observations; Mathematical finance; Parametric inference; Stochastic volatility

Indexed keywords

EID: 0000808770     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318447     Document Type: Article

References (23)

1. Bamdorff-Nielsen, O.E. (1978) Hyperbolic distribution and distribution on hyperbolae. Scand. J. Statist., 5, 151-157.
2. Barndorff-Nielsen, O.E. and Sorensen, M. (1994) A review of some aspects of asymptotic likelihood theory for stochastic processes. Int. Statist. Rev., 62, 133-165.
3. Bibby, B. and Sorensen, M. (1995) Martingale estimation functions for discretely observed diffusion processes. Bernoulli, 1, 17-39.
4. Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. J. Political Economy, 81, 637-659.
5. Blattberg, R. and Gonedes, N. (1974) A comparison of the stable and Student distributions as statistical models for stock prices. J. Business, 47, 244-280.
6. Chesney, M. and Scott, L. (1989) Pricing European currency options: A comparison of the modified Black-Scholes model and a random variance model. J. Financial Quant. Anal., 24, 267-289.
7. Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A theory of term structure of interest rates. Econometrica, 53, 385-407.
8. Dacunha-Castelle, D. and Duflo, M. (1983) Probabilités et Statistiques, Vol. 2, Problèmes àTemps Mobile. Paris: Masson.
9. Dacunha-Castelle, D. and Florens-Zmirou, D. (1986) Estimation of thé coefficient of a diffusion from discrete observations. Stochastics, 19, 263-284.
10. Donahl, G. (1987) On estimating the diffusion coefficient. J. Appl. Probab., 24, 105-114.
11. Genon-Catalot, V and Jacod, J. (1993) On thé estimation of the diffusion coefficient for multidimensional diffusion processes. Ann. Inst. Henri Poincaré, Probab.-Statist., 29, 119-151.
12. Genon-Catalot, V, Jeantheau, T. and Larédo, C. (1998) Limit theorems for discretely observed stochastic volatility models. Bernoulli, 4, 283-303
13. Ghysels, E., Harvey, A. and Renault, E. (1996) Stochastic volatility. Handbook Statist., 14, 119-192.
14. Heston S.L. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud., 6, 327-343.
15. Hull, J. and White, A. (1987) The pricing of options on assets with stochastic volatilities. J. Finance, 42, 281-300.
16. Kessler, M. (1996) Simple and explicit estimating functions for a discretely observed diffusion process. Prépublication du Laboratoire de Probabilités de l'Université de Paris VI.
17. Kessler, M. (1997) Estimation of an ergodic diffusion from discrete observations. Scand. J. Statist., 24(2), 211-229
18. Kutoyants, Yu.A. (1984) Parameter Estimation for Stochastic Processes. Berlin: Heldermann.
19. Larédo, C. (1990) A sufficient condition for asymptotic sufficiency of incomplete observations of a diffusion process. Ann. Statist., 18, 1158-1171.
20. Luke, Y.L. (1969) Tlie Special Functions and Tlieir Approximations. Math. Sci. Engng, 53. New York: Academic Press.
21. Madan, D.B. and Seneta, E. (1990) The variance gamma model for share market returns. J. Business, 63, 511-524
22. Nelson, D.B. (1990) ARCH models as diffusion approximations. J. Econometrics, 45, 7-38.
23. Rogers, L.C.G. and Williams, D. (1987) Diffusions, Markov Processes and Martingales. Vol. 2, Ito Calculus. Wiley Ser. Probab. Math. Statist. New York: Wiley