Estimation in Financial Models - RiskLab

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Bibliography [1] Ball, C.A., 1993, \A Review of Stochastic Volatility Models with Application to Option Pricing", Financial Markets, Institutions and Instruments, Vol. 2, No. 5, pp. 55-71. [2] Basawa, I.V. and B.L.S. Prakasa Rao, 1980, \Statistical Inference for Stochastic Processes", Academic Press Inc. [3] Bernardo, J.M. and A.F.M. Smith, 1994, \Bayesian Theory", Wiley, New York. [4] Bibby, B.M, 1994, \A Two-Compartment Model with Additive White Noise", Research Report No.290, Dept. Theor. Statist., University of Aarhus. [5] Bibby, B.M, 1994, \Optimal Combination of Martingale Estimating Functions for Discretely Observed Diusion Processes", Research Report No.298, Dept. Theor. Statist., University of Aarhus. [6] Bibby, B.M., 1995, \Analysis of a Tracer Experiment Based on Compartmental Diusion Models", Research Report No.303, Dept. Theor. Statist., University of Aarhus. [7] Bibby, B.M., 1995, \On Estimation in Compartmental Diusion Models", Research Report No.305, Dept. Theor. Statist., University of Aarhus. [8] Bibby, B.M and M. Srensen, 1995, \Martingale Estimation Functions for Discretely Observed Diusion Processes", Bernoulli Vol. 1 No.(1/2), pp. 17-39. [9] Billingsley, P., 1986, \Probability and Measure", 2nd ed., Wiley, New York. 79
[10] Billingsley,P., 1968, \Convergence of Probability Measures", Wiley, New York. [11] Black, F., 1990, \Living up to the model", Risk Magazine, Mar 1990. [12] Bollerslev, T., 1986, \Generalized Autoregressive Conditional Heteroskedasticity", Journal of Econometrics 31, pp. 307-327. [13] Bollerslev, T., R.Y. Chou and K.F. Kroner, 1992, \ARCH Modeling in Finance", Journal of Econometrics 52, pp. 5-59. [14] Bollerslev, T., R.F. Engle and D.B. Nelson, 1994, \ARCH Models", The Handbook of Econometrics, Vol. 4. [15] Breiman, L., 1968, \Probability", Addison-Wesley Publishing Company. [16] Brockwell, P.J. and R.A. Davis, 1987, \Time Series: Theory and Methods", Springer-Verlag, New York. [17] Cramer, H., 1946, \Mathematical Methods of Statistics", Princeton University Press. [18] Dacunha-Castelle, D. and M. Duo, 1993, \Probabilites et Statistiques", Masson, Paris. [19] Dacunha-Castelle, D. and D. Florens-Zmirou, 1986, \Estimation of the Coecients of a Diusion from Discrete Observations", Stochastics 19, pp. 263-284. [20] Deelstra, G. and G. Parker, 1995, \A Covariance Equivalent Discretisation of the CIR Model", Proceedings of the 5th AFIR International Colloquium, Vol.2, pp. 731-747. [21] Due, D. and K.J. Singleton, 1995, \An Econometric Model of the Term Structure of Interest Rate Swap Yields", Working paper, Graduate School of Business, Stanford University. [22] Engle, R.F., 1982, \Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Ination", Econometrica 50, pp. 987- 1008. [23] Engle, R.F. and M. Rothschild, 1992, \ARCH Models in Finance", Journal of Econometrics, Annals 1992-1, Vol. 52. [24] Feigin, P.D., 1976, \Maximum Likelihood Estimation for Continuoustime Stochastic Processes', Adv. Appl. Probab., Vol. 8, pp. 712-736. 80
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Estimation in Financial Models RISK
Page 3 and 4:
5 Some Diusion Models with Explicit
Page 5 and 6:
ing functions or methods based on a
Page 7 and 8:
wonder why people still use the Bla
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Chapter 2 Approximations 2.1 Diusio
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1) fX kh g: the family of discrete
Page 13 and 14:
By means of Theorem 1we now obtain
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2.2 Discrete time models by diusion
Page 17 and 18:
Chapter 3 Parameter Estimation 3.1
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which in the case (3.6) has the for
Page 21 and 22:
(see [49], p.249f). Asymptotic norm
Page 23 and 24:
a convergence in probability result
Page 25 and 26:
time between observations is bounde
Page 27 and 28:
For xed 0 s < t, x 2 IR d , 2 an
Page 29 and 30: After these theoretical considerati
Page 31 and 32: Considering the system (3.26) we di
Page 33 and 34: An Application As an application of
Page 35 and 36: If depends on we use the same est
Page 37 and 38: The asymptotic properties of the es
Page 39 and 40: Corollary 2 For we have F (X (i,1)
Page 41 and 42: disadvantage of ~G n and G n motiv
Page 43 and 44: 3.2 Discrete models In section 1.2
Page 45 and 46: The sequence hMi n is called the sq
Page 47 and 48: of time varying variances and covar
Page 49 and 50: The Hessian is @ 2 l t @@ 0 = , 1 @
Page 51 and 52: 3.2.3 The Bayesian estimation metho
Page 53 and 54: f() with respect to (jx). If 1 ; 2
Page 55 and 56: p( 1 j 2 ) and we have the a priori
Page 57 and 58: Chapter 4 Nonparametric Estimation
Page 59 and 60: for model (4.2) and the estimator ^
Page 61 and 62: Chapter 5 Some Diusion Models with
Page 63 and 64: and thus X t = t;t0 X t0 + Z t t 0
Page 65 and 66: If we do not specialize at this poi
Page 67 and 68: where we assume the choice of b 1 b
Page 69 and 70: where h is given by (5.42). Again w
Page 71 and 72: Appendix A The Kalman-Bucy Filter A
Page 73 and 74: A.2 The discrete case For reasons o
Page 75 and 76: we can write the Euler scheme (B.1)
Page 77 and 78: Appendix C The It^o Formula C.1 The
Page 79: Appendix D The Radon-Nikodym Theore
Page 83 and 84: [38] Ibragimov, I.A. and R.Z. Has'm
Page 85: [63] Pedersen, A.R., 1994, \Statist
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