Abstract
It is well known that the Black-Scholes model is used to establish the behavior of the option pricing in the financial market. In this paper, we propose the modified version of Black-Scholes model with two assets based on the Liouville-Caputo fractional derivative. The analytical solution of the proposed model is investigated by the Laplace transform homotopy perturbation method.
Highlights
A derivative is one of the financial instruments promising payment at a certain time in the future and the payoff amount depends upon the change of some underlying asset
We focus on the time fractional Black-Scholes model with two assets for the European call option
The fractional Black-Scholes equations is a generalized version of the classical model which extend the restriction of using the model for finding the option price
Summary
A derivative is one of the financial instruments promising payment at a certain time in the future and the payoff amount depends upon the change of some underlying asset. Proposed the Black-Scholes model to investigate the behaviour of the option pricing in a market. Several Mathematical models based on the Black-Scholes equation with five-key components of the strike price, the risk-free rate, the underlying security stock price, the volatility and the mature time have been developed [4,5,6,7]. One of the methods to solve the Black-Scholes equations is radial basis function partition of unity method (RBF-PUM) [17,18] which widely uses to approximate the partial differential equation problem. The Black-Scholes model with 2 assets for option pricing can be written as follows:. (LHPM) to obtain the explicit solution of the time fractional Black-Scholes model. We focus on the time fractional Black-Scholes model with two assets for the European call option.
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