## SENSITIVITY ANALYSIS OF CALL OPTION OBTAINED BY FRACTIONAL BLACK-SCHOLES EQUATION DERIVED BY FRACTIONAL BROWNIAN MOTION AND ITÔ’S FORMULA APPROACH

Published: 2018-02-14

Page: 70-84

AASIYA LATEEF *

Department of Mathematics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, India.

C. K. VERMA

Department of Mathematics and Computer Applications, Maulana Azad National Institute of Technology, Bhopal, India.

*Author to whom correspondence should be addressed.

### Abstract

Fractional order Black Scholes equation is growing day by day in financial market analysis and become an important part of the financial theory. By replacing the standard Brownian motion in classical Black Scholes equation with Fractional Brownian motion, we can get Fractional Black Scholes equation. Classical Financial models are based on semi martingale processes of stationary and independent increments which are not suitable for empirical investigations. So Fractional Brownian Motion was introduced as one of the stochastic models. Fractional Brownian motion is used to denote a family of Gaussian random functions and characterized by its covariance function and Hurst parameter H∈ (0,1). For values of H different than 1/2, fBm is not a semi martingale and classical Itô’s formula does not suitable in that case. This gives rise to obtain fractional It ’s formulas. In this paper we have calculated Call Option price by Fractional Black-Scholes equation driven by Fractional Brownian Motion and ItÔ’s formula approach with the help of MATLAB. Sensitivity Analysis has been performed with the help of three dimensional graphs on the results of Option Pricing in the form of Option Greeks namely Delta, Gamma, Theta, Vega, and Rho.

Keywords: Fractional Black-Scholes equation, Fractional Brownian motion, Itô’s formula, option Greeks

#### How to Cite

LATEEF, A., & VERMA, C. K. (2018). SENSITIVITY ANALYSIS OF CALL OPTION OBTAINED BY FRACTIONAL BLACK-SCHOLES EQUATION DERIVED BY FRACTIONAL BROWNIAN MOTION AND ITÔ’S FORMULA APPROACH. Asian Journal of Mathematics and Computer Research, 23(2), 70–84. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/864