Quiz For Lecture # 11
European Call Option using Black-Scholes/Merton
Consider a European call option on a stock when there are ex-dividend dates in two
months and five months. The dividend on each ex-dividend date is expected to be $ 0.50.
The current share price is $50 and the strike price is $50. The stock price volatility is 20%
per annum and the risk free rate is 8.329% per annum, the volatility is continuously
compounded, the interest rate is a simple interest rate, the time to maturity is six months.
Calculate the call option's price and delta using Black-Scholes/Merton.
(Reminder: Showing the essential steps along the way will enhance your chances of
partial credit in case you make an error.)1
 r 
r = n ⋅ ln 1 + 1 
n

d y = 0.5 ⋅ e
2
−0.08 ⋅
12
0.08=1 · ln (1+0.08329/1)
+ 0.5 ⋅ e
5
−0.08 ⋅
12
c0 = (S0 -d y ) ⋅ N (d1 ) − Ke
− rf T
= 0.9770
N (d 2 )
where
 S0 − d y  
σ2 
ln 
+ rf +
T
K  
2 

and
d1 =
σ T
d 2 = d1 − σ T
S0 = 50, K = 50, rf= 0.08, σ = 0.2, T = 0.5.
We can use the discounted dividend of 0.977 and deduct it from the spot price of the
stock. Using the B-S/M formula on a dividend-paying stock,
d1 =
 0.2 2  6 
 50 − 0.977  
 ⋅ 

ln
0.08
+
+
 

50
 

 2  12 
6
0.2 ⋅
12
= 0.2140
and
d2 = d1 - 0.2√0.5 =
0.0.0726
1
This question is taken from a former midterm exam. It was worth 25% of the entire midterm.
1
This implies that:
N(d1) = 0.58, N(d2) = 0.53
so that the call price c0 from the B-S/M formula is:
c0 = (50-0.977) · 0.58 - 50 · 0.53 · e-0.08 x 0.5 = 3.26.
2