In: Finance
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 .
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 |