Problems
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Skill-Building Problems.
1. The current stock price of a company is $54.50, the continuous annual standard deviation was
53.00%, the exercise price of an European call on the stock is $58.00, the exercise price of an
European put on the stock is $58.00, the time to maturity for both options is 0.43 years, and the
yield on a riskfree Treasury Bill maturing on the same date at the options is 6.72%. Determine the
current prices of the call and put.
2. Perform instant experiments on whether changing various inputs causes an increase or decrease in
the Call Price and in the Put Price and by how much.
(a.) What happens when the standard deviation is increased?
(b.) What happens when the time to maturity is increased?
(c.) What happens when the exercise price is increased?
(d.) What happens when the riskfree rate is increased?
(e.) What happens when the dividend yield is increased?
(f.) What happens when the standard deviation is really close to zero?
(g.) What happens when the time to maturity is really close to zero?
3. The current stock price of a company is $39.25, the continuous annual standard deviation was
47.00%, the exercise price of an European call on the stock is $36.00, the exercise price of an
European put on the stock is $36.00, the time to maturity for both options is 0.82 years, the yield
on a riskfree Treasury Bill maturing on the same date at the options is 4.23%, and the continuous
dividend paid throughout the year at the rate of 2.40% / year rate. Determine the current prices of
the call and put.
4. The S&P 500 index closes at 2000. European call and put options on the S&P 500 index with the
exercise prices show below trade for the following prices:
Exercise price 1,950 1,975 2,000 2,025 2,050
Call price $88 $66 $47 $33 $21
Put price $25 $26 $32 $44 $58
All options mature in 88 days. The S&P 500 portfolio pays a continuous dividend yield of 1.56%
per year and the annual yield on a Treasury Bill which matures on the same day as the options is
4.63% per year. Determine what is the implied volatility of each of these calls and puts. What
pattern do these implied volatilities follow across exercise prices and between calls vs. puts?
Live In-class Problems.
17. Given the partial Basics spreadsheet BsoptbaZ.xls, complete step 2 d1 and d2 Formulas, 3
Cumulative Normal Formulas, and 4 European Call Price Formula.
18. Given the partial Continuous Dividend spreadsheet BsoptdiZ.xls, do steps 2 Modify the d1
Formula, 3 Modify the Call Price Formula, and 4 Modify the Put Price Formula.
19. Given the partial Dynamic Chart spreadsheet BsoptdyZ.xls, do steps 10 Option Price and 11
Add the Intrinsic Value.
20. Given the partial Implied Volatility spreadsheet BsoptimZ.xls, do steps 6 Call Up Excel Solver,
7 Set-up Solver, 8 Run Solver, and 9 Repeat.
Skill-Building Problems.
1. The current stock price of a company is $54.50, the continuous annual standard deviation was
53.00%, the exercise price of an European call on the stock is $58.00, the exercise price of an
European put on the stock is $58.00, the time to maturity for both options is 0.43 years, and the
yield on a riskfree Treasury Bill maturing on the same date at the options is 6.72%. Determine the
current prices of the call and put.
2. Perform instant experiments on whether changing various inputs causes an increase or decrease in
the Call Price and in the Put Price and by how much.
(a.) What happens when the standard deviation is increased?
(b.) What happens when the time to maturity is increased?
(c.) What happens when the exercise price is increased?
(d.) What happens when the riskfree rate is increased?
(e.) What happens when the dividend yield is increased?
(f.) What happens when the standard deviation is really close to zero?
(g.) What happens when the time to maturity is really close to zero?
3. The current stock price of a company is $39.25, the continuous annual standard deviation was
47.00%, the exercise price of an European call on the stock is $36.00, the exercise price of an
European put on the stock is $36.00, the time to maturity for both options is 0.82 years, the yield
on a riskfree Treasury Bill maturing on the same date at the options is 4.23%, and the continuous
dividend paid throughout the year at the rate of 2.40% / year rate. Determine the current prices of
the call and put.
4. The S&P 500 index closes at 2000. European call and put options on the S&P 500 index with the
exercise prices show below trade for the following prices:
Exercise price 1,950 1,975 2,000 2,025 2,050
Call price $88 $66 $47 $33 $21
Put price $25 $26 $32 $44 $58
All options mature in 88 days. The S&P 500 portfolio pays a continuous dividend yield of 1.56%
per year and the annual yield on a Treasury Bill which matures on the same day as the options is
4.63% per year. Determine what is the implied volatility of each of these calls and puts. What
pattern do these implied volatilities follow across exercise prices and between calls vs. puts?
Live In-class Problems.
17. Given the partial Basics spreadsheet BsoptbaZ.xls, complete step 2 d1 and d2 Formulas, 3
Cumulative Normal Formulas, and 4 European Call Price Formula.
18. Given the partial Continuous Dividend spreadsheet BsoptdiZ.xls, do steps 2 Modify the d1
Formula, 3 Modify the Call Price Formula, and 4 Modify the Put Price Formula.
19. Given the partial Dynamic Chart spreadsheet BsoptdyZ.xls, do steps 10 Option Price and 11
Add the Intrinsic Value.
20. Given the partial Implied Volatility spreadsheet BsoptimZ.xls, do steps 6 Call Up Excel Solver,
7 Set-up Solver, 8 Run Solver, and 9 Repeat.