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Question 1 A call option has an exercise price of $ 1 0 . 0 0 and an expiry date of six months. The underlying

Question 1
A call option has an exercise price of $10.00 and an expiry date of six months. The underlying stock is currently trading for $12.00.
(a) What is the minimum price an investor would pay for this option? Could an investor
profit if the call option was actually trading at $1.00?
(b) What is the maximum price an investor would pay for this option? If the option was
trading for $13.00, how could an investor earn a risk-free profit?
This is a more analytical question than a quantitative one.
Question 2
A call option has a striking price of $8.10 and an expiry date of six months. The underlying stock is
currently trading at $7.60 and has historically exhibited a standard deviation of 10.6 percent. The
standard deviation is not expected to change. The interest rate is 5.4 percent. Using the Black-Scholes equation, estimate the value of the call option described above. What are some of the limitations of using the Black-Scholes equation?
Question 3
Suppose you have just purchased a share of stock in WYZ Corp for $50. The stock is not expected to pay a dividend during the time you plan to hold it. You have forecasted that the stock will be worth in one year either $ 65 or $40. Suppose further that you can sell a call option on WYZ stock with an exercise price of $52.50. It is a European-style contract that expires in exactly one year. What the option should sell for today if the one-year T-bill yield is 8%?
Question 4
Suppose that WYZ stock is currently valued at $53 and that call and put options on WYZ stock with an exercise price of $50 sell for $6.74 and $2.51 respectively. Both options can only be exercised in 6 months. You can also buy a 6-month T-bill with a $50 face value with an annualized rate/return of 6.25%. Does Put-Call parity hold? If not, what is the arbitrage trade you should make and what is the arbitrage profit? Please answer all this with the necessary math work.Show working

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