Valuation of American Option with Discrete Dividend Payments

An option is a type of financial derivative that gives its holder the right to buy or sell the underlying asset when the payoff is positive to them. Options are the most traded financial derivative in the exchanges all over the world. Its importance to the derivatives market has led to numerous researches conducted on option valuation. Several pricing models have been developed, such as binomial model and Black-Scholes model. The Black-Scholes model is a stochastic differential equation that gives option values based on the price of underlying asset at any time to option's maturity. European options can be valued by solving the BlackScholes model analytically, as European options are only allowed to be exercised upon maturity. Conversely, American options can be exercised any time before maturity date. Hence, it is more efficient to value American options using numerical methods, such as the finite difference method. This paper considers lognormal stock price process and discrete dividend payments on the stock. The partial differential equation is then discretized using finite difference approximations and solved within the domains for stock prices and time to maturity. The results are then presented graphically on the option prices at any time to maturity date. Warrants from Malaysia are selected to visualize the pricing of warrants using the Black-Scholes model.