No abstract

No abstract

Black-Scholes (BS) equations, which are in the form of stochastic partial differential equations, are fundamental equations in mathematical finance, especially in option pricing. Even though there exists an analytical solution to the standard form, the equations are not straightforward to be solved numerically. The effective and efficient numerical method will be useful to solve advanced and non-standard forms of BS equations in the future. In this paper, we propose a method to solve BS equations using an approach of optimization problems, where a metaheuristic optimization algorithm is utilized to find the best-approximated solutions of the equations. Here we use the Adaptive Differential Evolution with Learning Parameter (ADELP) algorithm. The BS equations being solved are meant to find values of European option pricing that is equipped with Barrier option pricing. The result of our approximation method fits well to the analytical approximation solutions.

Option can be defined as a contract between two sides/parties said party one and party two. Party one has the right to buy or sell of stock to party two. Party two can invest by observe the put option price or call option price on a time period in the option contract. Black-Scholes option solution using finite difference method based on forward time central space (FTCS) can be used as the reference for party two in the investment determining. Option price determining by using Black-Scholes was applied on Samsung stock (SSNLF) by using finite difference method FTCS. Daily data of Samsung stock in one year was processed to obtain the volatility of the stock. Then, the call option and put option are calculated by using FTCS method after discretization on the Black-Scholes model. The value of call option was obtained as $1.457695030014260 and the put option value was obtained as $1.476925604670225.

No abstract