Question

You are attempting to value a call option with an exercise price of $150 and one year to expiration. The underlying stock pays no dividends. Its current price is $100. The stock price either increases by a factor of 1.5, or decreases by a factor of 0.5, every six months. The risk-free rate of interest is 2% per year (or 1% per six-month period). What is the value of this call option using the two-period binomial option pricing model? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Answer 1

first we have to arrive p = probability for price increase, , (1-p) = probability for price decrease.,

P= (i -d) / (u-d),

no information about compounding, so it is assumed that continuous compoundig is used, then i = e^rt , d = 0.5, u = 1.5 are given in question.

e^{(0.02X 6/12)}, = 1.01005016708417.

=(1.01005016708417 - 0.5) / (1.5 - 0.5),

p =  0.51005016708417

Value at each intermediate node = (Value at upper node X p X e^-rt) + (Value at lower node X (1-p) X e^-rt) Value at$150 = ($75 X 0.51005016708417 X e^-0.01 ) + 0 X 0.48994983291583 X e^-0.01 )= 37.8694061409057,

Since profit @ $75 and @25 are zero, the corresponding values are also zero.,

no need to examine early exercise of option at the price of$150, becaues if the stock price and strike price equals, cannot exercise the option.

Next the value at The price of $100 = (37.8694061409057 X 0.51005016708417 X 0.990049833749168) + 0 = 19.1231065139141,

The value of option = $19.123

Please rate the answer maximum if you get the answer and satisfied. If you remains any doubts on this answer, please leave a comment and it will be cleared.

Thank you,…