About subordinated generalizations of 3 classical models of option pricing
Mathematica Applicanda, Tome 52 (2024) no. 1, pp. 3-25
Cet article a éte moissonné depuis la source Annales Societatis Mathematicae Polonae Series
In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the inverse subordinators. Such models, in contrast to their classical equivalents, can be used in markets where periods of stagnation are observed. We introduce the subordinated Cox-Ross-Rubinstein model and prove that the price of the underlying in that model converges in distribution and in Skorokhod space to the price of underlying in the subordinated Black-Scholes model defined in [24]. Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.
@article{10_14708_ma_v52i1_7256,
author = {Micha{\l} Balcerek and Grzegorz Piotr Krzy\.zanowski and Marcin Magdziarz},
title = {About subordinated generalizations of 3 classical models of option pricing},
journal = {Mathematica Applicanda},
pages = { 3--25},
year = {2024},
volume = {52},
number = {1},
doi = {10.14708/ma.v52i1.7256},
language = {pl},
url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v52i1.7256/}
}
TY - JOUR AU - Michał Balcerek AU - Grzegorz Piotr Krzyżanowski AU - Marcin Magdziarz TI - About subordinated generalizations of 3 classical models of option pricing JO - Mathematica Applicanda PY - 2024 SP - 3 EP - 25 VL - 52 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.14708/ma.v52i1.7256/ DO - 10.14708/ma.v52i1.7256 LA - pl ID - 10_14708_ma_v52i1_7256 ER -
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Michał Balcerek; Grzegorz Piotr Krzyżanowski; Marcin Magdziarz. About subordinated generalizations of 3 classical models of option pricing. Mathematica Applicanda, Tome 52 (2024) no. 1, pp. 3-25. doi: 10.14708/ma.v52i1.7256
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