S^a : ASM Exercise 22.15

The time-t price of a stock is S(t). You are given

The risk-neutral process for S(t) is

dS(t) = .15S(t) dt + .32 S(t)d Z_squiggle (t)



Where Z_squiggle (t) is a standard Brownian motion int he risk-neutral measure.



The stock pays dividends of .01S(t) dt between times t and t+dt.

S(0) = 10.



A special put option allows the purchaser to sell S(.25) shares of the stock at time .25 for 100. Determine price of this option.



Solution:

S shares of S are worth S^2. The forward price of S^2, using the risk-neutral process for S, is calculated to be 100e^.1006



We deduce that since .15 = r-dividend, r=.16.

We proceed with the Black-Scholes formula.



N(-d1) = .31762

N(-d2) = .43866



P = 100e^(-.16*.25 ) * .43866 - 100e^(.1006-.16*.25) * .31762 = 8.4



My question: why is the bolded .16 used? Shouldn't it instead be the dividend, .01?

I am using the formula

P=Ke^[-r(T-t)] * N(-d2) - S_t e^[-div(T-t) ] *N(-d1)



Where S_t=100e^.1006 ?

S^a : ASM Exercise 22.15