NO.PZ202304100300003202
问题如下：
The value of the American-style put option on Beta
Company shares is closest to:
选项：
A.4.53.
5.15.
9.32.
解释：
Using the expectations approach, the
risk-neutral probability of an up move is
π= [FV(1) - d]/(u - d) = (1.03 - 0.800)/(1.300 - 0.800) = 0.46.
An American-style put can be exercised early. At
Time Step 1, for the up move, p+ is 0.2517
and the put is out of the money and should not be exercised early (X <S, 40 < 49.4). However, at Time Step 1, p-is 8.4350 and the put is in the money by 9.60 (X - S = 40 - 30.40). So, the put is exercised early, and
the value of early exercise (9.60) replaces the value of not exercising early
(8.4350) in the binomial tree. The value of the put at Time Step 0 is now
p = PV[πp+ + (1 -
π)p-]
= [1/(1.03)][0.46(0.2517) + 0.54(9.60)] = 5.1454.
Following is a supplementary note regarding
Exhibit 1.
The values in Exhibit 1 are calculated as
follows.
At Time Step 2:
p++ = Max(0,X - u2S) = Max[0,40 - 1.3002(38)] =
Max(0,40 - 64.22) = 0.
p-+ = Max(0,X - udS) = Max[0,40 - 1.300(0.800)(38)] = Max(0,40 - 39.52) =
0.48.
p- - = Max(0,X - d2S) = Max[0,40 - 0.8002(38)] =
Max(0,40 - 24.32)= 15.68.
At Time Step 1:
p+ = PV[πp++ + (1 - π)p-+] =
[1/(1.03)][0.46(0) + 0.54(0.48)] = 0.2517.
p- = PV[πp-+ + (1 - π)p- -] =
[1/(1.03)][0.46(0.48) + 0.54(15.68)]=8.4350.
since 8.4350 < 9.60 (X - S = 40 - 30.40), so p- = 9.60
At Time Step 0:
p = PV[πp+ + (1 - π)p-]
= [1/(1.03)][0.46(0.2517) + 0.54(9.60)] = 5.1454.
题干只说call option exercise price 40， put option exercise price哪儿来的？
