Pricing Gap options using Black-Scholes

in section 14.2.2, Pricing Gap Options using Black-Scholes, of the ASM Manual, we are given the formula:



d1= [ln (Se^-(δT) / K_2 * e^(-rT) ) +T*.5*σ^2] / (σ*T^(.5))

and d2= d1-σ*T^(.5)



Solving Quiz 14 -2 (pg 342), we are given

For a 1-year gap put option, you are given:

Stock price = 40

δ=0

r=.08

σ=.3

K_2 / Trigger = 45



Using Black-Scholes pricing, calculate the strike price that makes the price of this option zero.



Why in the solution do they use the formula for d1 as

d1= [ln(S/K) + (r-δ+.5*σ^2)T ] / (σ*T^(.5))

instead of the bolded formula above?



Thanks!

Pricing Gap options using Black-Scholes