Abstract:
Option pricing is one of the most important concerns in the world of finance. An
option is an agreement between two parties to buy or sell an asset at a certain strike
price in the future. Option can be classified into two types based on the sort of rights
possessed by the holder, which are Call Option and Put Option. One method for
calculating the option value is to use the Black Scholes model. Analytically resolving
this equation can be difficult, particularly for more complicated option and market
circumstances. One method that can be used in such situations is the finite difference
method. This technique offers numerical solutions for option under actual market
conditions and enables the computation of increasingly complex option values. This
study aims to determine the option price using the explicit finite difference method
applied to Tesla company stock price data. The results obtained from the explicit
finite difference method will then be compared with the analytical method calculated
using the Black-Scholes model. The analysis of the Black-Scholes equation using the
explicit finite difference method highlights its performance and stability across
different time steps. Using a grid partition of = = 5, the method closely approximates
the analytical values at = 0.2, resulting in minimal error with 0.0189 at = 300 for
both Call and Put Option with mean of the error analysis are 1.0014 for Call Option
and 0.2080 for Put Option. But the result significantly deviates at = 1 for both Call
and Put Option. Leading to the largest error with 24.7095 at = 120 and the mean of
the error analysis is 13.0183 for the Call Option. And for the Put Option, the largest
error is 16.2287 at = 60 and the mean of the error analysis is 6.2927. This result
consistent for both call and put options reinforce these findings, indicating that while
the explicit finite difference method provides accurate approximations at earlier time
steps.
