Geodesic
Study of European style options under Itô-McKean Brownian motion with Azzalini skew-normal distribution
Filomat, Tome 36 (2022) no. 17, p. 5843

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In this article, we deal European style option, with arbitrary payoff which includes both put and call options, on an asset whose price evolves as Itô-McKean skew Brownian motion with Azzalini skew-normal distribution. Initially, we investigate a condition which leads the Itô-McKean skew Brownian motion to be a martingale. Next, we price the option and show that if the payoff function is convex then so is the price function. After this, we show if the payoff is finite then the price function satisfies a partial differential equation with respect to time. Further, we provide a necessary and sufficient condition for the price function to satisfy Feymann-Kac type equation. Next, we study Black-Scholes type equation and give expressions for the delta hedge. Finally, we study the particular case of an European call option in order to compare some of our results with the existing literature. Our results can be used to investigate the optimal exercise boundary, discrete time hedging strategies etc. of the option.
DOI : 10.2298/FIL2217843H
Classification : 60G44, 60J70, 91G50
Keywords: Itô-McKean Skew Brownian Motion, Martingales, European Option, Value Function, Feymann-Kac Formula, Black- Scholes Equation, Delta Hedge 
Sultan Hussain; Nasir Rehman; Faryal Fatima; Muhammad Shoaib Saleem. Study of European style options under Itô-McKean Brownian motion with Azzalini skew-normal distribution. Filomat, Tome 36 (2022) no. 17, p. 5843 . doi: 10.2298/FIL2217843H
@article{10_2298_FIL2217843H,
     author = {Sultan Hussain and Nasir Rehman and Faryal Fatima and Muhammad Shoaib Saleem},
     title = {Study of {European} style options under {It\^o-McKean} {Brownian} motion with {Azzalini} skew-normal distribution},
     journal = {Filomat},
     pages = {5843 },
     year = {2022},
     volume = {36},
     number = {17},
     doi = {10.2298/FIL2217843H},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2217843H/}
}
TY  - JOUR
AU  - Sultan Hussain
AU  - Nasir Rehman
AU  - Faryal Fatima
AU  - Muhammad Shoaib Saleem
TI  - Study of European style options under Itô-McKean Brownian motion with Azzalini skew-normal distribution
JO  - Filomat
PY  - 2022
SP  - 5843 
VL  - 36
IS  - 17
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2217843H/
DO  - 10.2298/FIL2217843H
LA  - en
ID  - 10_2298_FIL2217843H
ER  - 
%0 Journal Article
%A Sultan Hussain
%A Nasir Rehman
%A Faryal Fatima
%A Muhammad Shoaib Saleem
%T Study of European style options under Itô-McKean Brownian motion with Azzalini skew-normal distribution
%J Filomat
%D 2022
%P 5843 
%V 36
%N 17
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2217843H/
%R 10.2298/FIL2217843H
%G en
%F 10_2298_FIL2217843H

Cité par Sources :