# 2021 First Sit

```Test First Sit EBC2053
Test ID: 40274
Folder: /Preview
Version: 1.15
Randomised: No
Number of questons: 11
Blocks: Fixed, Display once
Display questions once: No
Tools: Spell checker browser, Calculator extended
Test time: 120 minutes
Maximum score: 121 pt.
Chance score: 0.50 pt. / 0%
In test set with: -
Declaration of Originality
Question order: Random
The Declaration of Originality has to be answered in the exam, but will be excluded in the grading process.
Question 1 − Declaration of Originality for Open questions_ start of exam − 27877.1.3
Declaration of Originality for online assessments
I hereby declare that the submitted exam will be produced independently by me, without external help.
In open questions I will use my own words. Wherever I paraphrase or cite literally, a reference to the original source (journal,
book, report, internet, etc.) is provided.
By agreeing with this statement, I explicitly declare that I am aware of the fraud sanctions as stated in the Education and
Examination Regulations (EERs) of Maastricht University. I am also aware that I should not share any information on the
exam questions or my answers with others during the official examination period.
A
I agree
B
I do not agree. I am aware of the consequences and that my exam will not be graded and will be considered as invalid
Page 1/5 - First Sit EBC2053 - 40274.1.15
Binomial Model
Question order: Fixed
Assume the following parameters for a binomial model (all parameters are in per period units, i.e.,
The price of the index today is
the volatility for the first period is
):
the risk-free interest today is
(continuously compounded), and the real-world probability for an up move is 90%.
In case the stock price goes up the parameters are
real-world probability for an up move is 93%.
(continuously compounded), and the
In case the stock price goes down the parameters are
(continuously compounded), and the
real-world probability for an up move is 93%.
The index pays a constant dividend yield of 3% per period (continuously compounded) over both periods.
Question 2 − First question binomial block − 74682.2.2
Price a European call option (at t=0) on the index with strike K=60 and maturity T=2, i.e., it matures in two periods. Use the
risk-neutral pricing equation for the valuation.
Criterion 1 (Number of points: 5)
Question 3 − Second question binomial block − 74695.1.0
Construct the tree containing the prices of the European option with K=60 and T=2.
Criterion 1 (Number of points: 5)
Question 4 − Third question binomial block − 74697.2.0
Set up a portfolio containing the European option with K=60 and T=2 and the index which results in a risk-free investment.
Show the value of the portfolio and its composition at each node of the tree. Finally, describe (shortly) the trades at each
node.
Criterion 1 (Number of points: 20)
Question 5 − Fourth question binomial block − 74707.1.0
Compute the forward price of the index for a forward with maturity T=2.
Criterion 1 (Number of points: 10)
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Black-Scholes Model
Question order: Fixed
Assume the underlying assumptions of the Black-Scholes model hold and use the following parameters for the index:
We want to analyze a European put option with strike K=60 and T=1.5 years.
Question 6 − First question Black−Scholes block − 74708.2.0
Set up a delta hedging portfolio for the put using:
1. The index
2. A futures contract on the index
Why would it be beneficial to use a futures contract?
Criterion 1 (Number of points: 5)
Question 7 − Second question Black−Scholes block − 74709.3.1
Evaluate the performance of your delta hedging strategy by computing and comparing the outcomes of the price changes if
the stock price increases by 5 instantaneously, i.e., no time passes. What is the problem?
Criterion 1 (Number of points: 10)
Question 8 − Third question Black−Scholes block − 74710.3.0
How do you improve the performance of the delta hedging strategy? Compute the new portfolio positions using your
proposed methodology. Show that the strategy performs better than a simple delta hedge if the stock increases by 5.
(HINT: The volatility is constant since we assume that the Black-Scholes model holds.)
Criterion 1 (Number of points: 15)
Question 9 − Fourth question Black−Scholes block − 74711.2.1
Assume you observe a second stock index with an identical dividend yield and an expected return of
Compute
the probability that a put option with strike K=60 and T=1.5 years will be exercised under the true probabilities for both
stock indices. Which of the puts will be more expensive and why?
Criterion 1 (Number of points: 10)
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Options in Practice
Question order: Fixed
SMPL Bank wants to start trading &quot;structured products&quot;. After doing some research they came across the following
description of a &quot;discount certificate&quot;:
Question 10 − First question options in practice − 74746.1.0
How can the discount certificate be replicated? Assume that the underlying is the AEX index for your answer.
Criterion 1 (Number of points: 15)
Question 11 − Second question options in practice − 74747.2.2
You used the current market data on AEX options to estimate the following model for implied volatilities
with
denoting the strike,
the current stock price, and
the time to maturity in years. This model applies to the
mid-prices of the options.
In addition, the current value for the AEX is 700 and the dividend yield is estimated to be 2.7% per year. This information
applies to the mid-price of the index.
Finally, assume the bid-ask spread to be 0.02 EUR for the index and 0.30 EUR for options traded on the index.
1. Compute the bid-ask prices for the discount certificate on the AEX index with one year to maturity and a cap that is 15%
above the current index value.
2. How should SMPL bank hedge the certificate?