Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
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Chapter 5, Problem 8AP
To determine
Effect on current account and world real interest rate.
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Consider a call option on a stock that does not pay dividends.
The stock price is $100 per share, and the risk-free interest rate is 10%.
The call strike is $100 (at the money).
The stock moves randomly with u=2 and d=0.5.
1. Write the system of equations to replicate the option using A shares and B bonds.
2. Solve the system of equations and determine the number of shares and the number of bonds
needed to replicate the option. Show your answer with 4 decimal places (x.xxxx); do not
round intermediate calculations. This is easy to do in Excel.
A =
B =
3. Use A shares and B bonds from the prior question to calculate the premium on the option.
Again, do not round intermediate calculations and show your answer with 4 decimal places.
Call premium =
Answer these questions using replication or the risk neutral probability. Both methods will
produce the same answer.
Show your work to receive credit.
6. What is the premium of a call with a higher strike.
Show your work to receive credit; do not round intermediate calculations.
S0 = $100, u=2, d=0.5, r=10%, strike=$150
Answer these questions using replication or the risk neutral probability. Both methods will produce the same answer.
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