Question

Suppose the price per share of Dans stock today is $30 and it is known that the price in three months will be either $20 or $35. If the strike price on a call option for one share of this stock is $28, the call option expires in three months, and the risk-free interest rate is 5%, determine the following based on the single-period binomial modelConsider another investor Pam who wants to acquire shares of Dans stock and has $600 to invest. What is Pams potential profit/loss (in today’s dollars)if Pam spends all of his money on

(a) shares of Dans stock?
(b) call options on shares of Dans stock?

Answer 1

A) Calculation of the probability of upside

p=30*e^0.05*3/12- 20/(35-20) = 0.69

q (Prob of downside) = 1- p =0.31

Number of shares which can be purchased 600/30 = 20

Expected Profit if all the money is invested in shares

= (35*.69*20+20*.31*20)-600 = 7

Value of call option are purchased =((35-28)*69+0*.31)/e^(0.25*3/12)= 4.77

Number of options which can be purchased = 600/4.77= 125.78

Profit/ Loss in option = ((35-28)*.69*125)+0-600=3.75

Hence the expected profit will be lesser in Options