Question

A stock price is currently $100. Over each of the next two 3-month periods it
is expected to go up or go down with up-factor u and down-factor d. The risk-free interest
rate is 6% per annum with continuously compounding. Consider a 6-month American put
option with a strike price of K.

Find the price of this American put option. Motivate your solutions, discuss early exercising decisions at each nodes prior to the maturity.

K = 100, u = 1.3, d = 0.9

Answer 1

Formulas Used :-

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$7)*((E13*$F$6)+($F$7*E17)),EXP(-$C$6*$C$7)*($C$4-D14))

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

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

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