Question

In: Finance

A binary call option pays $1 at expiry if the value of the underlying asset is...

A binary call option pays $1 at expiry if the value of the underlying asset is greater than the strike price, and $0 otherwise. The current interest rate is 3% pa.

(a) Calculate the return R over one month.

(b) Calculate all state prices at expiry for a ten-step binomial model where each time step is one month and the underlying asset is S=20, K=19, u=1.090, d=0.9173. That is, calculate all λ(10, j) for j = 0, 1, . . . , 10 .

Solutions

Expert Solution

a)

Return over month for example for first month = (21.8-20)/20= 9%

b) Ten Step Binomial model lattice

47.34727
43.43787
39.85125 39.84555
36.56078 36.55555
33.542 33.53721 33.53241
30.77248 30.76808 30.76368
28.23163 28.2276 28.22356 28.21952
25.90058 25.89688 25.89317 25.88947
23.762 23.7586 23.7552 23.75181 23.74841
21.8 21.79688 21.79377 21.79065 21.78753
20 19.99714 19.99428 19.99142 19.98856 19.9857
18.346 18.34338 18.34075 18.33813 18.33551
16.82879 16.82638 16.82397 16.82157 16.81916
15.43705 15.43484 15.43263 15.43042
14.1604 14.15838 14.15635 14.15433
12.98934 12.98748 12.98562
11.91512 11.91341 11.91171
10.92974 10.92818
10.02585 10.02441
9.196711
8.436143
T = 0 T = 1 T = 2 T =3 T = 4 T = 5 T = 6 T = 7 T = 8 T = 9 T = 10

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