Investigation of Effects of Asset Price Fluctuations on Option Value

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.