Test First Sit EBC2053 Test ID: 40274 Folder: /Preview Version: 1.15 Randomised: No Last modified: Monday, 31 may 2021 13:38:00 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. Grading instruction 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. Grading instruction 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. Grading instruction 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. Grading instruction Criterion 1 (Number of points: 10) Page 2/5 - First Sit EBC2053 - 40274.1.15 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? Grading instruction 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? Grading instruction 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.) Grading instruction 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? Grading instruction Criterion 1 (Number of points: 10) Page 3/5 - First Sit EBC2053 - 40274.1.15 Options in Practice Question order: Fixed SMPL Bank wants to start trading "structured products". After doing some research they came across the following description of a "discount certificate": 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. Grading instruction 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? Grading instruction Criterion 1 (Number of points: 25) Page 4/5 - First Sit EBC2053 - 40274.1.15 Page 5/5 - First Sit EBC2053 - 40274.1.15 Powered by TCPDF (www.tcpdf.org)
