Question

16. A call option has X-$45 and expire in 115 days. The risk-free rate is 4.5%. The call is priced at $9.00. A put option has X-$45 and is priced at $3.75. The underlying asset is priced at $50. Which of the following statement is correct? A. There is no arbitrage opportunity B. There is arbitrage loss and whoever invest will lose a lot C. There is arbitrage profit and whoever invest will gain a lot D. It cannot be determined whether or not arbitrage opportunity exist E. None above 17. The three-month call with X-$90 is priced at $5. The three-month call with X-$100 is priced at $3. What is the maximum possible profit on a bullish spread strategy? A. $5 B. $7 C. $8 D. $10 E. None above 18. For a put option, which one of the following factor will increase the put option's premium for sure? A. Longer expiration date B. Higher Volatility C. Lower Exercise Price D. All above E. None above 19 Which of the following statement is true? A. For any type of option strategy, the payoffs will never be negative B. For any type of option strategy, the profit will never be negative C. There is no option strategy that guarantees positive profit D. There is no option strategy that guarantees positive payoffs E. None above 20. In a covered call strategy: A. The payoff is greater than the profit B. The payoff is the same as the profit C. The payoff is lower than the profit D. The payoff and profit has no relation E. None above 4

Answer 1

Strike price=   45  
Time in days/365= 115/365      
risk free rate=   4.50%  
r for 115 days= 4.5%*115/365=   0.01417808219  
Continuous compounded rate (e^r) formula =(r)^1/ 1 + (r)^2 / (2*1) + (r)^3 / (3*2*1) + (r)^4 / (4*3*2*1)      
(0.01417808219)^1 /1 + ((0.01417808219)^2 / (2*1) )+ ((0.01417808219)^3 / (3*2*1)) + ((0.01417808219)^4 / (4^3*2*1))      
0.01427906652      
      
Value of call at X= 45=   9  
value of put at X=45=   3.75  
Stock.price=   50  
      
As per put call parity = Current market price + Put option value = (Excercise price/(1+e^i))+call option value      
50+3.75 = (45/(1+0.01427906652))+9.00      
53.75 is not Equal to   53.36648797  
LHS and RHS is not equal. so there is arbirtage opportunity. whoever will use arbitrage strategy, will definitely gain of 53.75-53.37=   0.38  
Correct answer is c. all other are wrong      
Other options : There can only be arbitrage profit, arbirtage loss can never happen, as a person will not invest definitely to loose money      
      
      

Note: first question is Answered as per HOMEWORKLIB POLICY