35 Black–Scholes and Dividends In addition to the five factors discussed in the chapter, dividends also affect the price of an option. The Black–Scholes option pricing model with dividends is:

C

= S ×  e −dt  × N( d 1 ) − E ×  e −Rt  × N( d 2 )

d 1 =  [ ln (S / E ) +(R − d +  σ 2 / 2 ) × t ] / (σ ×  √

_ t ) .

d 2

=  d 1  − σ ×  √

_ t

All of the variables are the same as the Black–Scholes model without dividends except for the variable d, which is the continuously compounded dividend yield on the share.

(a) What effect do you think the dividend yield will have on the price of a call option? Explain.

(b) Genmab A/S is currently priced at 2.26 Danish Kroner (DKr) per share, the standard deviation of its return is 50 per cent per year, and the risk-free rate is 5 per cent per year compounded continuously.

What is the price of a call option with a strike price of DKr2.00 and a maturity of six months if the share has a dividend yield of 2 per cent per year?