Abstract:
In this paper, the numerical effects of asset price fluctuation on the value of an
option using a two-dimensional Black-Scholes-Merton partial differential equation
have been investigated. The equation governing the value of an option was solved
numerically using the Crank-Nicolson finite difference scheme and simulated in
MATLAB software to obtain the profiles of the option values. The numerical
results obtained from the present study have been presented graphically and also
discussed. The effects of varying risk-free interest rate, the volatility of the two
assets prices, correlation coefficient between the two asset prices, and dividend
payout on the value of an option have been determined. It was observed that an
increase in volatility of the two asset prices results in an increase in the values of
both the call and put options. It was also noted that an increase in risk-free interest
rate results in an increase in the value of a call option but a decrease in the value
of a put option. Furthermore, the results revealed that an increase in the dividend
payout and correlation coefficient between the two asset prices results in a decrease
in the value of a call option but an increase in the value of a put option. The results
obtained from the present study are useful for investors wishing to maximize the
profits from their investments.
