The Calibration of Some Stochastic Volatility Models Used in Mathematical Finance

Show more

References

[1] Einstein, A. (1905) über die von der molekularkinetischen theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik, 322, 549-560.

http://dx.doi.org/10.1002/andp.19053220806

[2] Keller, J.B. (1964) Wave propagation in random media. Proceedings of Symposia in Applied Mathematics, 13, 227-246.

[3] Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-659.

http://dx.doi.org/10.1086/260062

[4] Kalman, R.E. (1960) A new approach to linear filtering and prediction problems. Journal of Basic Engineering-Transactions of the ASME, Series D, 85, 35-45.

http://dx.doi.org/10.1115/1.3662552

[5] Bachelier, L. (1900) Théorie de la speculation. Annales Scientifiques de l’école Normale Supérieure, 3, 21-86.

[6] Merton, R.C. (1973) Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141-183.

http://dx.doi.org/10.2307/3003143

[7] Hull, J. and White, A. (1987) The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281-300.

http://dx.doi.org/10.1111/j.1540-6261.1987.tb02568.x

[8] Stein, E.M. and Stein, J.C. (1991) Stock price distribution with stochastic volatility: An analytic approach. Review of Financial Studies, 4, 727-752.

http://dx.doi.org/10.1093/rfs/4.4.727

[9] Heston, S.L. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies, 6, 327-343.

http://dx.doi.org/10.1093/rfs/6.2.327

[10] Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A theory of the term structure of interest rates. Econometrica, 53, 385-407.

http://dx.doi.org/10.2307/1911242

[11] Hagan, P.S., Kumar, D., Lesniewski, A.D. and Woodward, E. (2002) Managing smile risk. Wilmott Magazine, 2002, 84-108.

http://www.wilmott.com/pdfs/021118_smile.pdf

[12] Cox, J. (1975) Notes on option pricing I: Constant elasticity of diffusions. Unpublished Draft, Stanford University.

[13] Harvey, A.C., Koopman, S.J. and Shephard, N. (2004) State space and unobserved component models: Theory and applications. Cambridge University Press, Cambridge.

[14] Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Ecometrica, 50, 1029-1054.

[15] Bollerslev, T. and Zhou, H. (2002) Estimating stochastic volatility diffusion using conditional moments of integrated volatility. Journal of Econometrics, 109, 33-65.

http://dx.doi.org/10.1016/S0304-4076(01)00141-5

[16] Jaynes, E.T. (1957) Information theory and statistical mechanics. Physical Review, 106, 620-630.

http://dx.doi.org/10.1103/PhysRev.106.620

[17] Shannon, C.E. (1948) A mathematical theory of communication. Bell System Technical Journal, 27, 379-423.

http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x

[18] Avellaneda, M. (1998) Minimum-relative-entropy calibration of asset pricing models. International Journal of Theoretical and Applied Finance, 1, 447-472.

http://dx.doi.org/10.1142/S0219024998000242

[19] Ait-Sahalia, Y. and Kimmel, R. (2007) Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics, 83, 413-452.

http://dx.doi.org/10.1016/j.jfineco.2005.10.006

[20] Bates, D.S. (2006) Maximum likelihood estimation of latent affine processes. The Review of Financial Studies, 19, 909-965.

http://dx.doi.org/10.1016/j.jfineco.2005.10.006

[21] Mariani, F., Pacelli, G. and Zirilli, F. (2008) Maximum likelihood estimation of the Heston stochastic volatility model using asset and option prices: An application of nonlinear filtering theory. Optimization Letters, 2, 177-222.

http://dx.doi.org/10.1007/s11590-007-0052-7

[22] Fatone, L., Mariani, F., Recchioni, M.C. and Zirilli, F. (2012) The use of statistical tests to calibrate the Black-Scholes asset dynamics model applied to pricing options with uncertain volatility. Journal of Probability and Statistics, 2012, Article ID: 931609.

[23] Johnson, R.A. and Bhattacharyya, G.K. (2006) Statistics: Principles and methods. 5th Edition, John Wiley & Sons, New York.

[24] Fatone, L., Mariani, F., Recchioni, M.C. and Zirilli, F. (2013) The use of statistical tests to calibrate the normal SABR model. Journal of Inverse and Ill-Posed Problems, 21, 59-84.

http://dx.doi.org/10.1515/jip-2012-0093

[25] Christoffersen, P., Heston, S. and Jacobs, K. (2009) The shape and term structure of the index option smirk: Why multifactor stochastic volatility models work so well. Management Science, 55, 1914-1932.

http://dx.doi.org/10.1287/mnsc.1090.1065

[26] Fatone, L., Mariani, F., Recchioni, M.C. and Zirilli, F. (2009) An explicitly solvable multi-scale stochastic volatility model: Option pricing and calibration problems. Journal of Futures Markets, 29, 862-893.

http://dx.doi.org/10.1002/fut.20390

[27] Mergner, S. (2009) Application of state space models in finance: An empirical analysis of the time-varying relationship between macroeconomics, fundamentals and Pan-European industry portfolios. Universitätsverlag Göttingen, Göttingen.