Question

There is a European put option in two months. The stock price is 58,u=0.2239 ,d=-0.183.The option has a strike price of 65, and the risk-free interest rate is a 5 percent annual percentage rate. What is the price of the put option today using one month steps?

Answer 1

Given That :

European Put Option

Stock Price (S) = 58

u = 0.2239 ie 1.2239

d= -0.183 ie 0.817

Strike Price (E) = 65

Risk Free Rate (r) = 5% p.a. ie 5/12 per month

Tie (t) = 2 months

R =(1+0.05)^2/12 = 1.0081648

Us = 58 x 1.2239 = 70.98

Ud = 58 x (1-0.183) = 47.38

Risk Neutral Probability ie P = R - d/ u-d

1.00816 - 0.817/ 1.2239 - 0.817 = 0.47

Pay off from Put if Price goes upto 70.98 (Pu)= 0

Pay of from Put if Price goes down to 47.38 (Pd)= (65 - 47.38) =17.62

Price of Put ie Po = P x Pu + (1 - P)xPd
R

= 0.47 x 0 + (1-0.47) x 17.62 / 1.00816

=$9.26