The Pricing Of American Call Option With Discrete Dividends

Options are one of the important fnancial derivations. The core problem aboutoptions is options pricing. In recent years, in order to adapt the fnancial market andsatisfy more investors, many scholars extend the Black-Scholes model to the case whereunderlying asset pays dividends. However, pricing the American option on dividendpaying asset is lack relatively. In this paper, we study the pricing formulas of the Americancall option, where underlying stock pays discrete dividends.Firstly, we introduce three diferent models to obtain closed-form option pricingformulas. Model1supposes that net-of-dividend stock price, that is the stock price minusthe present value of future dividends, follows a geometric Brownian motion. Model2suggests that cum-dividend stock price, defned as the stock price plus the forward valuesof the dividends paid from today up to maturity, follows a geometric Brownian motion.Model3suggests that discrete dividends is replaced by continuous dividend yield byusing Taylor expansion. The aim of the models3is the stock price at maturity followsthe lognormal distribution.Secondly, we study the pricing formulas of the American call option when interestrate is constant and underlying asset pays discrete dividends during the life of the option.We obtain the pricing formulas of the American call option by using risk-neutral valuationprincipal.Thirdly, we discuss the pricing formulas of the corresponairy American call optionwhen interest rate follow Vasicek model. We get the pricing formulas of the Americancall option by equivalent martingale measure transformation and the Girsanov theorem.