Answer:
Current value of this newly issued option on Internet Enterprises= $25
Explanation:
Risk free rate for 6 month or period 1= (1000-909.09)/909.09=10%
Risk free rate for 1 year= (1000-826.45)/826.45=21%
Hence, risk free rate for period 2= (1+21%)/(1+10%)-1=10%
Now, Risk free rate factor for period 1 (R1)=1+10%=1.1
Risk Free rate factor for period 2 (R2)=1+10%=1.1
Upward price factor for a period(u)=(1+100%)^(1/2)=1.414
Downward price factor for a period(d)=(1-50%)^(1/2)=0.707
Probability of upward price= (R-d)/(u-d)=(1.1-0.707)/(1.414-0.707)=0.55
Probability of downward price= 1-0.55=0.45
After period 1: Upward price=100*1.414=141.4 with probability 55%
Downward price =100*0.707=70.7 with probability 45%
After period 2:
Upward Price will be =141.4*1.414=200 with probability= 55%*55%=30.25%
Downward price will be=70.7*0.707=50 with probability=45%*45%=20.25%
Mid price will be = 141.4*0.707 or 70.7*1.414=100 with probability =2*45%*55%=49.5%
Now, the highest price the stock can go is $200 with probability 30.25% and it was issued at $100
Hence, expected payoff of the option=30.25%*(200-100)=$30.25
So, current value of the newly issued option= 30.25/(1+21%)=$25
