Question

Question 31

The stock price of Comet Inc. is currently $30. The stock price a year from now will be either $50 or $10 with equal probabilities. The interest rate at which investors can borrow is 5%. Using the binomial option pricing model (OPM), the value of a call option with an exercise price of $40 and an expiration date one year from now should be worth what?

Group of answer choices

between $4.50 and $5.00

less than $3.50

between $4.00 and $4.50

between $3.50 and $4.00

between $5.00 and $5.50

Answer 1

Strike or excercise price =   $40  
Current Market price =    $30  
Risk-free rate =    5%  
Time to Expiration=    1 year  
Rate for 1 months (r) = 5%*1= 5%      
Continuous compounded rate (e^r) formula =(r)^1/ 1 + (r)^2 / (2*1) + (r)^3 / (3*2*1) + (r)^4 / (4*3*2*1)      
(5%)^1 /1 + ((5%)^2 / (2*1) )+ ((5%)^3 / (3*2*1)) + ((5%)^4 / (4^3*2*1))      
0.05127088216      
Possible upside price (UP) =   50  
Possible downside price (DP)=   $10  
Value of call option = Stock price at Expiration -Strike price(subject to 0, value cannot be negative)      
VC at UP = 50-40=    10  
VC at DP = 10-40=   0  
Call detlta = (VC at upper - VC at lower)/(Upper price - downside price)      
(10-0)/(50-10)      
0.25      
Call option price as per binomial model= (Current Market price - (downside price/(1+e^i)))* Call delta      
(30-(10/(1+0.05127088216)))*0.25      
5.121925954      
So call option price is $5.12 according to binomial model.      
      

Answer is e, between $5.00 and $5.50