Sequential calibration of options

Computational Statistics and Data Analysis

Volumn 52, Issue 6, 2008, Pages 2877-2891

  Lindström, Erik ^a   Ströjby, Jonas ^a   Brodén, Mats ^a   Wiktorsson, Magnus ^a   Holst, Jan ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

Calibration; Non linear Kalman filters; Option valuation

Indexed keywords

KALMAN FILTERS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; STATISTICAL METHODS; VALUE ENGINEERING;

NON-LINEAR KALMAN FILTERS; OPTION VALUATION; VALUATION MODELS;

SEQUENTIAL SWITCHING;

EID: 39049128891     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.08.009     Document Type: Article

References (40)

1. Abramowitz, M., Stegun, I.A. (Eds.), 1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Dover, New York.
2. Anderson B.D.O., and Moore J.B. Optimal Filtering (1979), Prentice-Hall, Englewood Cliffs, NJ
3. Bakshi, G., Carr, P., Wu, L., 2007. Stochastic risk premiums: stochastic skewness in currency options, and stochastic discount factors in international economics. J. Financial Econom., in press, doi:10.1016/j.jfineco.2006.12.001.
4. Bakshi G.S., Cao C., and Chen Z. Empirical performance of alternative option pricing models. J. Finance 52 5 (1997) 2003-2049
5. Barndorff-Nielsen O.E. Processes of Normal inverse Gaussian type. Finance and Stochastics 2 (1997) 41-68
6. Barndorff-Nielsen O.E., and Shepard N. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J. Roy. Statist. Soc. Ser. B 63 (2001) 167-241
7. Barndorff-Nielsen O.E., and Shepard N. Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J. Roy. Statist. Soc. Ser. B 64 (2002) 253-280
8. Bates D. Jumps and stochastic volatility: the exchange rate processes implicit in Deutchemark options. Rev. Financial Stud. 9 (1996) 69-107
9. Black F., and Scholes M. The pricing of options and corporate liabilities. J. Political Economy 81 (1973) 637-659
10. Campbell J.Y., Lo A.W., and MacKinley A.C. The Econometrics of Financial Markets (1997), Princeton University Press, Princeton, NJ
11. Carr P., and Madan D. Option valuation using the fast Fourier transform. J. Comput. Finance 2 4 (1999) 61-73
12. Carr P., and Wu L. The finite moment log stable process and option pricing. J. Finance 58 (2003) 753-778
13. Carr P., and Wu L. Time-changed Lévy processes and option pricing. J. Financial Econom. 71 (2004) 113-141
14. Carr, P., Wu, L., 2007. Stochastic skew in currency options. J. Financial Econom., in press, doi:10.1016/j.jfineco.2006.03.010.
15. Carr P., Geman H., Madan D., and Yor M. The fine structure of asset returns: an empirical investigation. J. Business 75 (2002) 305-332
16. Carr, P., Geman, H., Madan, D., Wu, L., Yor, M., 2003a. Option pricing using integral transforms. A slideshow presentation available at: 〈http://www.math.nyu.edu/research/carrp/papers/pdf/integtransform.pdf〉.
17. Carr P., Geman H., Madan D., and Yor M. Stochastic volatility for Lévy processes. Math. Finance 13 (2003) 345-382
18. Chernov M., Gallant A.R., Ghysels E., and Tauchen G. Alternative models for stock price dynamics. J. Econometrics 116 (2004) 225-257
19. Cont R., and Tankov P. Financial Modelling with Jump Processes (2004), Chapman & Hall, London
20. Derman E., and Kani I. Riding on a smile. Risk 7 2 (1994) 32-39
21. Doucet, A., de Freitas, N., Gordon, N. (Eds.), 2001. Sequential Monte Carlo Methods in Practice. Springer, New York.
22. Draper N.R., and Smith H. Applied Regression Analysis. third ed. (1998), Wiley, New York
23. Duffie D., Pan J., and Singleton K. Transform analysis and asset pricing for affine jump diffusions. Econometrica 68 (2000) 1343-1376
24. Dupire B. Pricing with a smile. Risk 7 1 (1994) 18-20
25. Heston S.L. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud. 6 (1993) 327-343
26. Huang J.-Z., and Wu L. Specification analysis of option pricing models based on time-changed Lévy Processes. J. Finance 59 (2004) 1405-1440
27. Hull J.C. Options, Futures, and Other Derivative Securities. fifth ed (2002), Prentice-Hall, Englewood Cliffs, NJ
28. Hull J.C., and White A. The pricing of options on assets with stochastic volatility. J. Finance 42 2 (1987) 281-300
29. Kalman R.E. A new approach to linear filtering and prediction problems. Trans. ASME Ser. D J. Basic Eng. 82 (1960) 35-45
30. Kalman R.E., and Bucy R.S. New results in linear filtering and prediction. Trans. ASME Ser. D J. Basic Eng. 83 (1961) 95-107
31. Kitigawa G. A self-organizing state-space-model. J. Amer. Statist. Assoc. 93 443 (1998) 1203-1215
32. Künsch H.R. State space and hidden Markov models. In: Barndorff-Nielsen O.E., Cox D.R., and Klüppelberg C. (Eds). Complex Stochastic Systems, Monographs on Statistics and Applied Probability vol. 87 (2001), Chapman & Hall, New York 109-173
33. Lee, R.W., 2004. Option pricing by transform methods: extensions, unification, and error control. J. Comput. Finance 7, 51-86, an augmented version is available at: 〈http://www.math.uchicago.edu/∼rl/dft.pdf〉.
34. Lefebvre T., Bruyninckx H., and De Schutter J. Kalman filters for non-linear systems: a comparison of performance. Internat. J. Control 77 7 (2004) 639-653
35. Lindström, E., Ströjby, J., Brodén, M., Wiktorsson, M., Holst, J., 2006. Sequential calibration of options. Technical Report 21, Centre for Mathematical Sciences, Lund University.
36. Madan D.B., and Seneta E. The variance Gamma (VG) model for share market returns. J. Business 63 (1990) 511-524
37. Maybeck, P., 1982. Stochastic Models, Estimation and Control, vols. 1-3. Academic Press, New York.
38. Merton R.C. Option pricing when the underlying stock returns are discontinuous. J. Financial Econom. 5 (1976) 125-144
39. Polson N.G., and Stroud J.R. Bayesian inference for derivative prices. Bayesian Statist. 7 (2003) 641-650
40. Schoutens, W., Simons, E., Tistaert, J., 2004. A perfect calibration! Now what? Wilmott Magazine, March.