In this paper, we investigate the relation between Bachelier and Black-Scholes (B-S) models driven by the infinitely divisible 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 (CRR) model and prove that it converges in distribution to the subordinated B-S model defined in \mbox{%DIFAUXCMD gajda . Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.
In this paper, we investigate the relation between Bachelier and Black-Scholes models driven by the infinitely divisible 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 to the price of underlying in the subordinated Black-Scholes model defined in 25 . Motivated by this fact we price the selected option contracts using the binomial trees. The results are compared to other numerical methods.
D
(B-S)
D
(CRR)
R
it
the price of the underlying in that model
R
subordinated B-S
price of underlying in the subordinated Black-Scholes
R
\mbox{%DIFAUXCMD gajda
25