Homework 7
Adapted from Fundamentals of Futures and Options Markets, 7th ed., John C. Hull.
Chapter 12
Consider a European call option on a nondividendpaying
stock where the stock price is $100, the
strike price is $90, the riskfree
rate is 3% per annum, the volatility is 25% per annum, and the time to
expiration is 4 months.
Q1: Calculate u, d, and p for a twostep tree using a spreadsheet. Hint: If the expiration is 4 months
and there are two steps, then the length of each step (dt) is 2 months (=2/12).
Q2: Find the option value using a twostep
tree in spreadsheet. Do not use Derivagem for this part.
Q3: Verify that Derivagem gives the same price (use BinomialEuropean
with tree steps = 2). Copy
paste the Derivagem output and the price tree after clicking "display tree."
Hint: If your price in part Q3 does not match your answer in Q2, then at least one of them is incorrect!
Q4: Use Derivagem to price the same option using 5, 50, 100, and 500 steps. Include the Derivagem
output. Do not include the trees because Derivagem won't display trees with more than 10 steps.
Q5: Calculate the BlackScholes
option price tree using Derivagem. Use Option Type =
BlackScholes
European.
Which number of steps in Q4 results in the closest price to the
BlackScholes
price?
Adapted from Fundamentals of Futures and Options Markets, 7th ed., John C. Hull.
Chapter 12
Consider a European call option on a nondividendpaying
stock where the stock price is $100, the
strike price is $90, the riskfree
rate is 3% per annum, the volatility is 25% per annum, and the time to
expiration is 4 months.
Q1: Calculate u, d, and p for a twostep tree using a spreadsheet. Hint: If the expiration is 4 months
and there are two steps, then the length of each step (dt) is 2 months (=2/12).
Q2: Find the option value using a twostep
tree in spreadsheet. Do not use Derivagem for this part.
Q3: Verify that Derivagem gives the same price (use BinomialEuropean
with tree steps = 2). Copy
paste the Derivagem output and the price tree after clicking "display tree."
Hint: If your price in part Q3 does not match your answer in Q2, then at least one of them is incorrect!
Q4: Use Derivagem to price the same option using 5, 50, 100, and 500 steps. Include the Derivagem
output. Do not include the trees because Derivagem won't display trees with more than 10 steps.
Q5: Calculate the BlackScholes
option price tree using Derivagem. Use Option Type =
BlackScholes
European.
Which number of steps in Q4 results in the closest price to the
BlackScholes
price?
