Abstract
The key aim of the paper is to show that how the efficiently the Reduced Differential Transform Algorithm (RDTA) can be employed to price the exotic financial options. In this paper we have computed the exact solution of the parabolic partial differential equation governing the dynamics of put-call parity in the mathematical theory of Asian options, by means of RDTA.
Highlights
An option is an agreement that allows the holder to buy or sell at a specified future time an underlying asset at a specified price
In this paper we have computed the exact solution of the parabolic partial differential equation governing the dynamics of put-call parity in the mathematical theory of Asian options, by means of Reduced Differential Transform Algorithm (RDTA)
To illustrate the basic concepts of the Reduced Differential Transform Method (RDTM), consider the following nonlinear partial differential equation written in an operator form
Summary
An option is an agreement that allows the holder to buy (call option) or sell (put option) at a specified future time (expiration or maturity time) an underlying asset at a specified price (strike or exercise price). Considering path dependent contingent claims in general setting, the PDE is a strongly degenerate parabolic equation in three dimensions (time, the underlying asset price, and the path-dependent variable). In this setting, the needed regularity seemed out of reach. Let Cfix (S, J, t) and Pfix (S, J, t) denote the price of the fixed strike arithmetic averaging Asian call option and put option, respectively. Their terminal payoff functions are given by. Taking into consideration of this method, it is possible to find an exact solution or a closed approximate solution of a differential equation
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