Nonparametric estimation of the diffusion coefficient of stochastic volatility models

Econometric Theory

Volumn 24, Issue 5, 2008, Pages 1174-1206

  Renò, Roberto ^a  

^a UNIVERSITY OF SIENA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49549095519     PISSN: 02664666     EISSN: 14694360     Source Type: Journal    
DOI: 10.1017/S026646660808047X     Document Type: Article

References (47)

1. Aït-Sahalia, Y. (1996) Nonparametric pricing of interest rate derivative securities. Econometrica 64, 527-560.
2. Aït-Sahalia, Y., P. Mykland, & L. Zhang (2005) How often to sample a continuous-time process in the presence of microstructure noise. Review of Financial Studies 18, 351-416.
3. Andersen, T., L. Benzoni, & J. Lund (2004) Stochastic Volatility, Mean Drift and Jumps in the Short-Term Interest Rate. Working paper, Northwestern University.
4. Andersen, T., T. Bollerslev, & F.X. Diebold (2003) Parametric and Nonparametric Volatility Measurement. Working paper. Forthcoming in L.P. Hansen & Y. Aït-Sahalia (eds.., Handbook of Financial Econometrics. North-Holland.
5. Andersen, T., T. Bollerslev, F. Diebold, & P. Labys (2003) Modeling and forecasting realized volatility. Econometrica 71, 579-625.
6. Bandi, F. (2002) Short-term interest rate dynamics: A spatial approach. Journal of Financial Economics 65, 73-110.
7. Bandi, F. & G. Moloche (2004) On the Functional Estimation of Multivariate Diffusion Processes. Working paper, University of Chicago and MIT.
8. Bandi, F. & P. Phillips (2003) Fully nonparametric estimation of scalar diffusion models. Econometrica 71, 241-283.
9. Bandi, F. & J. Russell (2006) Separating microstructure noise from volatility. Journal of Financial Economics 79, 655-692.
10. Barndorff-Nielsen, O.E. & N. Shephard (2002) Econometric analysis of realised volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society, Series B 64, 253-280.
11. Barucci, E. & R. Renò (2002a) On measuring volatility and the GARCH forecasting performance. Journal of International Financial Markets, Institutions and Money 12, 183-200.
12. Barucci, E. & R. Renò (2002b) On measuring volatility of diffusion processes with high frequency data. Economics Letters 74, 371-378.
13. Chan, K., A. Karolyi, F. Longstaff, & A. Sanders (1992) An empirical comparison of alternative models of the short-term interest rate. Journal of Finance 47, 1209-1227.
14. Chapman, D., J. Long, & N. Pearson (1999) Using proxies for the short rate: When are three months like an instant? Review of Financial Studies 12, 763-806.
15. Cox, J., J. Ingersoll, & S. Ross (1985) A theory of the term structure of interest rates. Econometrica 53, 385-406.
16. Duffee, G. (1996) Idiosyncratic variation of Treasury bill yield spread. Journal of Finance 51, 527-552.
17. Fan, J. (2005) A selective overview of nonparametric methods in finance. Statistical Science 20, 317-337.
18. Fan, J. & C. Zhang (2003) A re-examination of Stanton's diffusion estimations with applications to financial model validation. Journal of the American Statistical Association 98, 118-134.
19. Florens-Zmirou, D. (1993) On estimating the diffusion coefficient from discrete observations. Journal of Applied Probability 30, 790-804.
20. Föllmer, H. (1981) Calcul d'Itô sans probabilités. Seminaire de Probabilites Strasbourg XV, Lecture Notes in Mathematics 850, pp. 143-150. Springer.
21. Hansen, P. & A. Lunde (2006) Consistent ranking of volatility models. Journal of Econometrics 131, 97-121.
22. Hansen, P., A. Lunde, & J.M. Nason (2003) Choosing the best volatility models: The model confidence set approach. Oxford Bulletin of Economics and Statistics 65, 939-961.
23. Härdle, W. (1990) Applied Nonparametric Regression. Cambridge University Press.
24. Hoffmann, M. (1999) Lp estimation of the diffusion coefficient. Bernoulli 5, 447-481.
25. Hull, J. & A. White (1987) The pricing of options on assets with stochastic volatility. Journal of Finance 42, 281-300.
26. Jacod, J. (1999) Non-parametric kernel estimation of the coefficient of a diffusion. Scandinavian Journal of Statistics 27, 83-96.
27. Jacod, J. & A.N. Shiryaev (1987) Limit Theorems for Stochastic Processes. Springer-Verlag.
28. Jeffrey, A., D. Kristensen, O. Linton, T. Nguyen, & P.C.B. Phillips (2004) Nonparametric estimation of a multifactor Heath-Jarrow-Morton model: An integrated approach. Journal of Financial Econometrics 2, 251-289.
29. Jiang, G. (1998) Nonparametric modeling of U.S. interest rate term structure dynamics and implications on the prices of derivative securities. Journal of Financial and Quantitative Analysts 33, 465-497.
30. Jiang, G. & J. Knight (1997) A nonparametric approach to the estimation of diffusion processes, with an application to a short-term interest rate model. Econometric Theory 13, 615-645.
31. Karatzas, I. & E. Shreve (1988) Brownian Motion and Stochastic Calculus. Springer-Verlag.
32. Knight, F.B. (1970) A reduction of continuous square integrable martingale to Brownian motion. In H. Dinges (ed.), Lecture Notes in Mathematics, Volume 190, pp. 19-31. Springer-Verlag.
33. Malliavin, P. & M. Mancino (2002) Fourier series method for measurement of multivariate volatilities. Finance and Stochastics 6, 49-61.
34. Malliavin, P. & A. Thalmaier (2005) Stochastic Calculus of Variations in Mathematical Finance. Springer Finance series. Springer.
35. Mancini, C. & R. Renò (2006) Threshold Estimation of Jump-Diffusion Models and Interest Rate Modeling. Manuscript, University of Florence and University of Siena.
36. Meddahi, N. (2002) A theoretical comparison between integrated and realized volatility. Journal of Applied Econometrics 17, 479-508.
37. Nielsen, M.O. & P.H. Frederiksen (2008) Finite sample accuracy and choice of sampling frequency in integrated volatility estimation. Journal of Empirical Finance 15, 265-286.
38. Priestley, M. (1979) Spectral Time Series Analysis. Wiley.
39. Renò, R. (2006) Nonparametric estimation of stochastic volatility models. Economics Letters 90, 390-395.
40. Renò, R., A. Roma, & S. Schaefer (2006) A comparison of alternative nonparametric estimators of the diffusion coefficient. Economic Notes 35, 227-252.
41. Revuz, D. & M. Yor (1998) Continuous Martingales and Brownian Motion. Springer-Verlag.
42. Scott, D. (1992) Multivariate Density Estimation. Wiley.
43. Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall/CRC.
44. Stanton, R. (1997) A nonparametric model of term structure dynamics and the market price of interest rate risk. Journal of Finance 52, 1973-2002.
45. Vasicek, O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics 5, 177-188.
46. Wand, M.P. & M.C. Jones (1995. Kernel Smoothing. Chapman and Hall.
47. Wiener, N. (1924. The quadratic variation of a function and its Fourier coefficients. Massachusetts Journal of Mathematics 3, 72-94.