Question

The current price of Natasha Corporation stock is $5.17. In each of the next two? years, this stock price can either go up by $2.50 or go down by $2.00. The stock pays no dividends. The? one-year risk-free interest rate is 4.4% and will remain constant. Using the Binomial? Model, calculate the price of a? two-year put option on Natasha stock with a strike price of $7.00.

Answer 1

First of all lets find probability of price moving up or down

U = Sou/So

=7.67/5.17

=1.4836

d = Sod/So

=3.17/5.17

=0.613

p = e^rt - d/ u-d

=(1.044) - 0.613/1.4836-0.613

=0.430847/0.870406

=49.5%

Thus probability of price increase is 49.5%

Probability of price decrease = 50.5%

Now

Fou = {fouu*p + foud*(1-p)]/1.044

=[0*0.495 + 1.33*0.505]/1.044

=0.67165/1.044

=0.6433

Now fod

=[fodu*p + fodd*(1-p)]/1.044

=[(1.33*0.495)+(5.83*0.505)]/1.044

=[0.65835+2.94415]/1.044

=3.6025/1.044

=3.4507

Now value of put option

=[fou*p + fod*(1-p)]/1.044

=[(0.6433*0.495) + (3.4507*0.505)]/1.044

=0.3184+1.7426 / 1.044

=2.06/1.044

=1.9742$