Finance 2 (2023) – Problem Set 5 (Week 6)
University of Amsterdam
Answers to IN CLASS exercises do not need to be handed in
The parts of exercises marked [IN CLASS] (e.g. 1d) will be completed during the tutorial
and answers to these parts do not need to be handed in via Canvas. Answers to the other
questions need to be completed before the deadline (see Canvas) and students need them
to participate in the tutorial.
Grading: only first problem set and bonus
We will only grade the first homework set in Canvas and then at the end of the course
determine if you have received the bonus or not. You will therefore not see a grade for
each homework set you have handed in. Feedback is possible during the tutorials.
Question 1 | Chapter 20/21 – Option valuation
You have a long position in a call option from a stock which currently trades at €60. The option has a
maturity of 6 months and an exercise price of € 70. The annual risk-free rate is 3%.
a. Explain (in detail) the rights or obligations that are implied by holding this position.
b. Assume that, in addition to the long position in the call option, you also hold a short position
in a put option on the same stock, with the same exercise price and the same exercise date.
Plot the payoff diagram of the combination of options that you hold.
Would you prefer the stock price to rise or fall until the exercise date?
c. Assume that the stock price can rise to €85 or stay at €60 during the next six month period.
Estimate the value of the call option using the replicating portfolio model. In your solution,
please explicitly write the equations for up and down states of the stock price.
Hint: correct the interest rate to match the maturity of the option.
d. What does the option delta (∆) in the replicating portfolio model indicate? [IN CLASS]
1
,Question 2 | Chapter 20 - Option valuation
Determine if the option value increases or decreases when each of the following five factors
increases? Complete the table below and give a short explanation.
Variable Value Long Call Value Long Put Explanation
Maturity Increases
Dividends
Volatility
Strike Price
Current Price Decreases
Question 3 | Chapter 20/21 – Option valuation
Assume you hold a portfolio of stocks that follows the AEX stock index perfectly. Today, you hear in
the news that the AEX might fall one month later, and you are worried about the losses you might
incur if that happens. You recall what you learned in the Finance course, and decide to use options
to reduce this risk. Assume the AEX index is currently valued at 480.
a. What type of option can you use to hedge against a drop in the AEX? Show the position
diagram at maturity for this strategy .
b. Suppose you read a research report stating that the AEX index will be subject to high
volatility in the near future. That is, you will see either large increases or large drops in its
value due to macroeconomic circumstances. More specifically, the value of the index will be
either larger than 500 or smaller than 410. What combination of options could be used to
profit from this information? Show the position diagram of this strategy at maturity.
c. Imagine now that the price of the AEX (currently valued at 480) can only go up with 10% or
down with 10% during the next period of four months. The risk-free rate is 5% per year. The
price of a European call option on the AEX with an exercise price of 450 and maturing in four
months is $30. Is the price of the call option fair? Use the replicating portfolio model to get
to your answer. [IN CLASS]
2
, Problem set 5
Question 1
You have a long position in a call option from a stock which currently trades at €60. The
option has a maturity of 6 months and an exercise price of €70. The annual risk-free rate
is 3%.
a.
A call option gives the right, but not the obligation, to buy the stock at the price of €70.
This option can be exercised up to and including the expiration date.
Assume that, in addition to the long position in the call option, you also hold a short
position in a put option on the same stock, with the same exercise price and the same
exercise date.
b.
University of Amsterdam
Answers to IN CLASS exercises do not need to be handed in
The parts of exercises marked [IN CLASS] (e.g. 1d) will be completed during the tutorial
and answers to these parts do not need to be handed in via Canvas. Answers to the other
questions need to be completed before the deadline (see Canvas) and students need them
to participate in the tutorial.
Grading: only first problem set and bonus
We will only grade the first homework set in Canvas and then at the end of the course
determine if you have received the bonus or not. You will therefore not see a grade for
each homework set you have handed in. Feedback is possible during the tutorials.
Question 1 | Chapter 20/21 – Option valuation
You have a long position in a call option from a stock which currently trades at €60. The option has a
maturity of 6 months and an exercise price of € 70. The annual risk-free rate is 3%.
a. Explain (in detail) the rights or obligations that are implied by holding this position.
b. Assume that, in addition to the long position in the call option, you also hold a short position
in a put option on the same stock, with the same exercise price and the same exercise date.
Plot the payoff diagram of the combination of options that you hold.
Would you prefer the stock price to rise or fall until the exercise date?
c. Assume that the stock price can rise to €85 or stay at €60 during the next six month period.
Estimate the value of the call option using the replicating portfolio model. In your solution,
please explicitly write the equations for up and down states of the stock price.
Hint: correct the interest rate to match the maturity of the option.
d. What does the option delta (∆) in the replicating portfolio model indicate? [IN CLASS]
1
,Question 2 | Chapter 20 - Option valuation
Determine if the option value increases or decreases when each of the following five factors
increases? Complete the table below and give a short explanation.
Variable Value Long Call Value Long Put Explanation
Maturity Increases
Dividends
Volatility
Strike Price
Current Price Decreases
Question 3 | Chapter 20/21 – Option valuation
Assume you hold a portfolio of stocks that follows the AEX stock index perfectly. Today, you hear in
the news that the AEX might fall one month later, and you are worried about the losses you might
incur if that happens. You recall what you learned in the Finance course, and decide to use options
to reduce this risk. Assume the AEX index is currently valued at 480.
a. What type of option can you use to hedge against a drop in the AEX? Show the position
diagram at maturity for this strategy .
b. Suppose you read a research report stating that the AEX index will be subject to high
volatility in the near future. That is, you will see either large increases or large drops in its
value due to macroeconomic circumstances. More specifically, the value of the index will be
either larger than 500 or smaller than 410. What combination of options could be used to
profit from this information? Show the position diagram of this strategy at maturity.
c. Imagine now that the price of the AEX (currently valued at 480) can only go up with 10% or
down with 10% during the next period of four months. The risk-free rate is 5% per year. The
price of a European call option on the AEX with an exercise price of 450 and maturing in four
months is $30. Is the price of the call option fair? Use the replicating portfolio model to get
to your answer. [IN CLASS]
2
, Problem set 5
Question 1
You have a long position in a call option from a stock which currently trades at €60. The
option has a maturity of 6 months and an exercise price of €70. The annual risk-free rate
is 3%.
a.
A call option gives the right, but not the obligation, to buy the stock at the price of €70.
This option can be exercised up to and including the expiration date.
Assume that, in addition to the long position in the call option, you also hold a short
position in a put option on the same stock, with the same exercise price and the same
exercise date.
b.
