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 mon...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 form bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation,). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rate r. 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.展开更多
文摘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 form bank. We see the influence of the dividend term on the option pricing via the comparison theorem of BSDE(backward stochastic differential equation,). We also consider the option pricing problem in terms of the borrowing rate R which is not equal to the interest rate r. 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.
