Question

comsider an american put option on a stock. the stock proce is 5, risk free ratr is 4% per annum, u= 1.05, d= .9524, p= 5912, and the ti,e to matuirty is three months.

value the oprion using a one step tree

Answer 1

I have solved it assuming a strike price which is same as stock price i.e 5 since not given. If it is different answer can be adjusted accordingly. Please get back to me incase of any further clarifications. Hope this helps. Happy learning

u = 1.05

d = 0.9524

t = 3/12 = 0.25

Rf = 4%

p = 59.12%

assuming strike price = 5

since it is a put option increase in stock price gives payoff of Fu = 0, whereas decrease in stock price gives payoff of Fd = (5*0.9524) - 5 = 0.238

put option value = e^-rt(p*Fu + 1-p * Fd)

= e^-(0.25)(.04)( 40.88% * 0.238) = 0.09632