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Master level 1 STUDENT N° : 20_M1_NI_FE_S2_CCO_805 Introduction to Derivatives FINAL ASSIGNMENT START DATE: 24/04/2020 4 pm (Paris time) DUE DATE: 11/05/2020 4 pm (Paris time) Professor/Lecturer: Laurent Deville INSTRUCTIONS: · SafeAssign : THIS ASSIGNMENT IS PROTECTED AGAINST PLAGIARISM · Assignment Type : Group assignment (groups of 2 students) · Assignment File(s) Type and Number : one DOCX, DOC or PDF file and one XLS file · Submission Attempts : 2 attempts Introduction to derivatives. Final assignment The objective of this assignment is to put in practice knowledge acquired within the course with real word data and situations. The actual covid-19 crisis give ample room for questions related to derivatives. For this final assignment, you will have to work in groups of 2 students. Should your personal situation prevent you from building a group, you can ask for an exception by sending a formal request to Manuela Balan detailing the reasons. Deliverables consist of a pdf or doc file containing your answers and an excel file containing your data and calculations. Note that the Excel spreadsheets serve only as a support to your analysis and will be used to check your calculations and numbers provided in the analysis. All explanations have to be detailed in the pdf/doc file. What will matter for the grading is the quality of the analysis not the length of the paper. You have to be able to justify your answers and show good understanding of the concepts. Exercise 1. Futures On Monday 20th April 2020, the WTI May 2020 futures contract (the US benchmark contract for oil) trading on NYMEX, fell from almost $18 per barrel to a lowest of -$40.32 per barrel (minus $40.32) over the course of the day. It finally settled at -$37.63. This exceptional event deserves some analysis, both from a theoretical and practical viewpoint. 1. Briefly summarize the specifications of the WTI futures contracts trading on NYMEX (size, settlement, termination of trading). What are the relevant dates for the May 2020 contract? 2. Explain precisely what an investor holding an outstanding long WTI may futures contract is committed to on that day and for the future. 3. At least one trade took place at -$40.32. What does it mean for counterparties? What would be the P/L for investors holding, before that trade, opposite outstanding positions (long or short) on that contract at $18 per barrel? 4. Based on the cash and carry relationship for investment assets, explain under which conditions a negative futures price for oil could be observable in theory. Under which condition(s) would a negative WTI futures price represent an arbitrage opportunity? Exercise 2. Options For this exercise, questions are independent. A. Put-Call Parity. Euronext provide quotes for CAC 40 index options at https://live.euronext.com/en/product/index-options/PXA-DPAR. 1. Extract data for all June and December option series in the middle of a trading day and briefly comment the trading activity. 2. Assuming PCP is verified, calculate the implied dividend yield using settlement values. Do you obtain the same average for both expiries? Briefly explain why this result was to be expected? B. Trading strategies With the covid-19 pandemic crisis, volatility has surged to very high levels after an extended period of historical low levels (see daily VIX index closing values from 2018 reported in Figure 1). It is a period where some investors are tempted to bet on a higher future volatility or, on the contrary, on declining future volatility levels. Figure 1. Daily VIX index Quotes for the SPX contract (European options on S&P 500 expiring on the 3rd Friday of the expiration month) are available on http://www.cboe.com/delayedquote/quote-table?ticker=spx. Based on these quotes, build 2 strategies that would prove profitable if, over the next month, the following event takes place: 1. volatility rebounds to highest levels observed at the beginning of the crisis 2. volatility plunges to pre-crisis levels. In both cases, build a strategy that is very aggressive (you have unlimited confidence on your expectation) and one that is less so (also you think that your prediction is accurate, you would prefer to limit your risks). For each strategy, represent the expiration payoff and calculate the initial value, break-even point, maximal expected profit and maximal loss. Without calculations, explain which sign is expected for the vega of your strategy. 3. Pricing options Pick up a stock that serves as an underlying for exchange traded option contracts. On the day of your choice, extract daily adjusted closing prices for the last year as well as the prevailing quotes for the at the money series with time to expiration closest to one month. To price the option with your model, you will need estimates of · Risk-free rate (use a relevant 1-month proxy such as Libor, Libor Euro, T-bill, …) · historical volatility (use annualized standard deviation of past returns using 1 year of data) · dividends (assume no dividend will be paid until expiration) Questions 1. Build a 4-step tree for the stock price until expiration using a conventional Cox-Ross-Rubinstein calibration 2. Price the closest to the money call option in the tree assuming its style is European 3. Price the corresponding European put option 4. It is very likely that you have found prices that defer (possibly very significantly) from market values. Explain the reason(s) that could explain why it is so. 5. Assuming your tree is an accurate representation of the world, how could you arbitrage away the differential between market prices and your estimates? Be extremely specific on which strategy you would follow and the amount of arbitrage profit you would obtain in the different states of the world. 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