Question

GS stock is currently worth $56. Every year, it can increase by 30% or decrease by 10%. The stock pays no dividends, and the annual continuously-compounded risk-free interest rate is 4%. Using a two-period binomial option pricing model, find the price today of one two-year European put option on the stock with a strike price of $120.

Answer 1

The binomial option of option pricing use following formula in calculation as,

for PUT option , the pay off at last , Max [ (K − S_n), 0 ]

At pay off at previous node,

Binomial Value = [p x Option up + (1 - p) x Option down] *exp(-- * At)

emin – d u-d d = e-ov

U= Increase 30%= 1.30

d= decrease 10%= 0.90

0.0121 - 0.90 P= = 0.3521 1.30 - 0.90

U^2*S=1.312*56 94.64 25.36 max(120-94.64,0) U*S=1.3*56 72.8 42.49182 56 U*d*S=1.30*0.9*56 65.52 54.48 max(120-65.52,0) 54.76836 d*S=0.9*56 50.4 (0.3521*42.49+(1- 0.3521)*64.892)*(2.72(-0.04)) 64.891821 d^2*S=0.912*56 45.36 74.64 max(120-45.36,0) Node Time: 0.0000 1.0000 2.0000

Value at T=0 , $ 54.77