Total for Question: 10 marks) Question 5 (10 marks) Consider the following infor

Question

Total for Question: 10 marks) Question 5 (10 marks) Consider the following information about a Current Stock Price S non-dividend paying stock. $20 40% per year 000 per year 3% per year Return Volatility Dividend Rate Risk-free Interest Rate Assume that the assumptions of the Black-Scholes model are met. Assume a risk-free zero- coupon bond with a 2-year maturity exists. A call option written on the non-dividend paying stock expires in 2 years and has an exercise price of $30. Find the Black-Scholes value of the call option using the provided a. cumulative normal density table with arguments rounded to two decimal places. (5 marks) b. Briefly explain why the out-of-money call option in part a) commands a premium. (2 marks) c. Given your answer in part a), find the Black-Scholes value of the corresponding put option with the same strike price and expiry (3 marks) (Total for question: 10 marks)

Explanation / Answer

Part (a)

Stock Price now (St)

20

Exercise Price of Option (K)

30

Number of periods to Exercise in years (t)

2

Compounded Risk-Free Interest Rate (rf)

3.00%

Standard Deviation (annualized s)

40.00%

Output Data

Present Value of Exercise Price (PV(K))

28.2529

s*t^.5

0.5657

d1

-0.3279

d2

-0.8935

Delta N(d1) Normal Cumulative Density Function

0.3715

Bank Loan N(d2)*PV(K)

5.2489

Value of Call option

2.1813

Part (b)

Options contract may be out of the money but eventually have value due to a significant change in the underlying asset's market price. This is known as the contract's time value.

Roughly translated, it signifies whatever price an investor is willing to pay above the contract's intrinsic value, in hopes the investment will eventually pay off. That’s why out of money call commands a premium.

Part (c)

Inputs are same as part (a) of solution.

Stock Price now (St)

20

Present Value of Exercise Price (PV(K))

28.2529

Value of Call

2.1813

Value of Put

=PV(K)+Value of Call-St

=28.2529+2.1813-20

=10.4342

Stock Price now (St)

20

Exercise Price of Option (K)

30

Number of periods to Exercise in years (t)

2

Compounded Risk-Free Interest Rate (rf)

3.00%

Standard Deviation (annualized s)

40.00%

Output Data

Present Value of Exercise Price (PV(K))

28.2529

s*t^.5

0.5657

d1

-0.3279

d2

-0.8935

Delta N(d1) Normal Cumulative Density Function

0.3715

Bank Loan N(d2)*PV(K)

5.2489

Value of Call option

2.1813

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