Malliavin calculus for the estimation of time-varying regression models used in financial applications

International Journal of Theoretical and Applied Finance

Volumn 10, Issue 5, 2007, Pages 771-800

  Abutaleb, Ahmed ^a   Papaioannou, Michael G ^b  

^a CAIRO UNIVERSITY   (Egypt)

^b INTERNATIONAL MONETARY FUND   (United States)

Author keywords

Clark Ocone formula; Malliavin calculus; Ornstein Uhlenbeck process; Stochastic calculus; Time series analysis; Time varying parameters

Indexed keywords

EID: 34548068321     PISSN: 02190249     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021902490700441X     Document Type: Article

References (28)

1. A. Abutaleb, Target image tracking using a nonlinear filter based on Pontryagin minimum principle, IEEE Trans. Automatic Control AC-31(12) (1986).
2. A. Abutaleb and M. Papaioannou, An adaptive filter for time-varying parameters models, International Journal of Adaptive Control and Signal Processing 4(5) (1990) 335-343.
3. A. Abutaleb and M. Papaioannou, Maximum likelihood estimation of time-varying parameters: An application to the Athens Exchange Index, Applied Economics 32(10) (2000) 1323-1329.
4. A. Abutaleb and M. Papaioannou, Malliavin calculus for the estimation of the US Dollar/Euro exchange rate when the volatility is stochastic, in Global Information Technology and Competitive Financial Alliances, eds. Y. Kurihara, S. Takaya and N. Yamori (IDEA Group Publishing 2006), pp. 71-101.
5. Y. Ait-Sahalia, Maximum likelihood estimation of discretely sampled diffusions; A closed form approximation approach, Econometrica 70(1) (2002) 223-262.
6. O. E. Barndoff-Nielsen and N. Shephard, Non-Gaussian Ornstein-Uhlenbeck- based models and some of their uses in financial economics, Journal of Royal Statistical Society Series B 63(2) (2001) 167-241.
7. F. E. Benth, Option pricing in the Barndoff-Nielsen and Shephard stochastic volatility model, paper presented at the workshop in Quantitative Finance at the Isaac Newton Institute, Cambridge University (2005).
8. H. Bermin, Essays on look back and barrier options, PhD. Dissertation, Lund University, Sweden (1998).
9. F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81 (1973) 637-659.
10. T. Bollerslev, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31 (1986) 307-327.
11. Y. Chen, C. Wen, J. Xu and M. Sun, High order iterative learning identification of projectile's aerodynamic drag coefficient curve from radar measured velocity data, IEEE Trans. Control Systems Technology 6(4) (1998) 563-570.
12. G. Chow, Econometrics (John Wiley, New York, 1987).
13. O. Elerian, Simulation Estimation of Continuous-Time Models with Applications to Finance, PhD Dissertation, University of Oxford, Nuffield College (1999).
14. O. Elerian, S. Chib and N. Shphard, Likelihood inference for discretely observed nonlinear diffusions, Econometrica 69(4) (2001) 959-993.
15. Y. Grenier, Time-dependent ARMA modeling of nonstationary signals, IEEE Trans. ASSP 31 (1983) 899-911.
16. I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. (Springer-Verlag, New York, 1991).
17. S. Neftci, An Introduction to the Mathematics of Financial Derivatives (Academic Press, New York, 2000).
18. M. Niedzwiecki, Identification of Time-Varying Processes (John Wiley, New York, 2000).
19. M. Niedzwiecki, Identification of time-varying systems using combined parameter estimation and filtering, IEEE Trans. ASSP 38(4) (1990) 679-686.
20. M. Niedzwiecki, On the localized estimators and generalized Akaike's criterion, IEEE Trans. Automatic Control AC-29 (1984) 970-983.
21. D. Nualart, The Malliavin Calculus and Related Topics (Springer-Verlag, New York, 1995).
22. D. Ocone and I. Karatzas, A generalized dark representation formula, with, application to optimal portfolios, Stochastics and Stochastics Reports 34 (1991) 187-220.
23. B. Oksendal, An introduction to Malliavin calculus with applications to economics, Working Paper 3/96, Institute of Finance and Management Science, Norwegian School of Economics and Business Administration (1996).
24. B. Oksendal, Stochastic Differential Equations: An Introduction with Applications, 3rd Edn. (Springer, New York, 1997).
25. B. Oksendal, Stochastic Differential Equations: An Introduction with Applications (Universitext, New York, 1998).
26. S. Shreve, Stochastic calculus and finance, Lecture notes (1996).
27. H. Van Dijk, A. Monfort and B. Brown, eds., Econometric Inference Using Simulation Techniques (John Wiley and Sons, New York, 1995).
28. H. Van Trees, Detection, Estimation and Modulation Theory (John Wiley, New York, 1968).