VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION
Penulis/Author
ABDUL HOYYI (1); Prof. Dr. Abdurakhman, S.Si., M.Si. (2); Prof. Dr.rer.nat. Dedi Rosadi, S.Si.,, M.Sc. (3)
Tanggal/Date
14 2022
Kata Kunci/Keyword
Abstrak/Abstract
T
he Option
is widely applied
in the financial sector.
The
Black
-
Sch
oles
-
Merton model i
s often used in calculating
option prices on a stock price movement. The model uses
geometric Brownian motion which assumes that the data is
normally distributed. However, in reality, stock price
movements can cause sharp spikes
in data, resulting in
non
normal data distribution. So we need a stock price model
that is not normally distributed.
One of the fastest growing
stock price models today is the
퐿
푒
̀
푣푦
process exponential
model.
The
퐿
푒
̀
푣푦
process has the ability to mode
l data that has
excess kurtosis and a longer tail (heavy tail) compared to the
normal distribution.
One of the members of the
퐿
푒
̀
푣푦
process
is the Variance Gamma (VG) process.
The VG process has
three parameters which each of them, to control volatility
,
kurtosis and skewness.
In this research, the secondary data
samples of options and stocks of two companies were used,
namely zoom video communications, Inc. (ZM) and Nokia
Corporation (NOK).
The price of call options is determined by
using closed form equations and Monte Carlo simulation. The
Simulation was carried out for various
푁
values until
convergent result was obtained.
