A BLACK-SCHOLES FORMULA FOR OPTION PRICING WITH DIVIDENDS

Abstract. We obtain a Black-Scholes formula for the arbitrage-free pricing of Eu-ropean Call options with constant coefficients when the underlylng stock generatesdividends. To hedge the Call option, we will always borrow money from bank. We seethe influence of the dividend term on the option pricing via the comparison theoremof BSDE(backward stochastic di~erential equation 5], 7]). We also consider the option pricing problem in terms of the borrowing rate R whichis not equal to the interest rate r. The corresponding Black-Sdxoles formula is given.We notice that it is in fact the borrowing rate that plays the role in the pricing formula.

A black-scholes formula for option pricing with dividends

We obtain a Black-Scholes formula for the arbitrage-free pricing of European Call options with constant coefficients when the underlying stock generates dividends. To hedge the Call option, we will always borrow money from bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation 5], 7]). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rater. The corresponding Black-Scholes formula is given. We notice that it is in fact the borrowing rate that plays the role in the pricing formula. This work was supported by the National Natural Science Foundation of China.