Question

Consider the following binomial option model. Stock price is 10 dollars now. In 1 year it can go to 12 dollars or 8 dollars. Interest rate with annual compounding is 10 percent. What is the price of a 1 year call with strike 11. .What are the risk-neutral probabilities? SHOW CALCULATIONS

Answer 1

We use 1 period binomial tree model here,

S₀=10, S_u=12, S_d=8

u = S_u/S₀ = 12/10 = 1.2

d= S_d/S₀ = 8/10 = 0.8

r=10% (annual compounding)

Risk neutral probabalities- {assuming annual compounding}

p=(1+r-d)/(u-d)=(1+10%-0.8)/(1.2-0.8) = 0.75

(1-p) = 1-0.75 = 0.25

Call price-

Call possibilities at t=1,

C₍₊₎ = MAX(S₍₊₎-K,0) = MAX(12-11,0) = 1

C_(-) = MAX(S_(-)-K,0) = MAX(8-11,0) = 0

Backsolving, call value at t=0,

C_t=0 = [p *C₍₊₎ + (1-p) * C_(-)]/(1+10%) =  [0.75 *1 + 0.25*0]/(1+10%) = $0.681818 (price of the call option using 1 period model)