Geodesic
Comparison of Certain Models and Results of Stochastic Financial Mathematics with Real Data
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 302-319 
V. N. Tutubalin. Comparison of Certain Models and Results of Stochastic Financial Mathematics with Real Data. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 302-319. http://geodesic.mathdoc.fr/item/TM_2002_237_a19/
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     author = {V. N. Tutubalin},
     title = {Comparison of {Certain} {Models} and {Results} of {Stochastic} {Financial} {Mathematics} with {Real} {Data}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Certain probabilistic models for the logarithmic increments of stock prices are compared with real data. It is shown that all these models are essentially inadequate because of the statistical instability of the observed data. Nevertheless, theoretical results on option hedging are confirmed (to unexpectedly high accuracy) by hedging simulations using real price data. This fact is explained by comparatively small fluctuations of the volatility of prices, which are the main source of imbalance (i.e. the hedging inaccuracy).

[1] Mandelbrot B. B., Fractals and scaling in finance. Discontinuity, concentration, risk, Springer-Verl., New York etc., 1997, 551 pp. | MR | Zbl

[2] Eberlein E., Keller U., Prause K., “New insights into smile, mispricing, and value at risk: the hyperbolic model”, J. Business, 71:3 (1998), 371–405 | DOI | MR

[3] Eberlein E., Recent advances in more realistic market and credit risk management: the hyperbolic model, Preprint Inst. Math. Stochastic Univ., Freiburg, 2000, Febr. 25

[4] Selezneva T. V., Tutubalin V. N., Uger E. G., “Issledovanie prikladnykh vozmozhnostei nekotorykh modelei stokhasticheskoi finansovoi matematiki”, Obozr. prikl. i promyshl. matematiki, 7:2 (2000), 210–238

[5] Shiryaev A. N., Osnovy stokhasticheskoi finansovoi matematiki. T. 1: Fakty. Modeli, Fazis, M., 1998; Т. 2: Теория

[6] Stepanov N. M., Volatilnosti i disbalansy pri khedzhirovanii optsionov, Dipl. rabota, Mekh.-mat. fak. MGU, M., 2000

[7] Lamburt V. G., “Sravnenie nekotorykh strategii khedzhirovaniya platezhnykh obyazatelstv, ispolzuyuschikh i ne ispolzuyuschikh martingalnuyu meru”, Obozr. prikl. i promyshl. matematiki, 8:1 (2001) | Zbl