- Option Pricing 185
Exercise 8.11. The ex-dividend stock prices are
n 012
158. 80
144. 00 <
S(n) 120. 00 < 115. 60
ex-div 108. 00 <
83. 20The corresponding European and American call values will be
n 012
38. 80
38. 80
23. 52
24. 00 <
CE(n)
CA(n)14. 25
14. 55
<^0.^00
0. 00
0. 00
0. 00
<
0. 00
0. 00
The American call should be exercised early in the up state at time 1 with
payoff 24 dollars (bold figures), which is more than the value of holding the
option to expiry. As a result, the price of the American call is higher than that
of the European call.
Exercise 8.12
Compute the prices of European and American puts with exercise and
strike priceX= 14 dollars expiring at time 2 on a stock withS(0) = 12
dollars in a binomial model withu=0.1,d=− 0 .05 andr =0.02,
assuming that a dividend of 2 dollars is paid at time 1.8.3 Black–Scholes Formula ....................................
We shall present an outline of the main results for European call and put
options in continuous time, culminating in the famous Black–Scholes formula.
Our treatment of continuous time is a compromise lacking full mathematical
rigour, which would require a systematic study ofStochastic Calculus, a topic