Question

There is an American put option on a stock that expires in two months. The stock price is $69 and the standard deviation of the stock returns is 59 percent. The option has a strike price of $78 and the risk-free interest rate is an annual percentage rate of 5.8 percent.

What is the price of the option? Use a two-state model with one-month steps. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Formulas Used:-

u=EXP(C5*SQRT(C6))

d=EXP(-C5*SQRT(C6))

p=(EXP(C6*C7)-F4)/(F3-F4)

1-p=1-F6

Stock(step-1)=C16*$F$3

Option(step-1)=MAX(EXP($C$6*$C$7)*($C$4-D14),(EXP(-$C$6*$C$7)*((E13*$F$6)+($F$7*E17))))

Stock(step-2)=C16*$F$4

Option(step-2)=MAX(EXP($C$6*$C$7)*($C$4-D18),(EXP(-$C$6*$C$7)*((E17*$F$6)+($F$7*E21))))

Option Value=(EXP(-$C$6*$C$7)*((D15*$F$6)+($F$7*D19)))

I hope my efforts will be fruitful to you.