1 CMSC 5718 Introduction to Computational Finance Assignment 3: Trading strategies and products (45% of total grade) Instructions 1) Submit a copy of your report together with supporting programs and/or data files (as a zipped file) by uploading to Blackboard on or before April 21, 2022, 11:59pm. The file name of the zipped file or your report should be your student number with the following format, e.g. 11550xxxxx.zip or 11551yyyyy.zip. [If uploading to Blackboard is not successful, you may consider sending a email to [email protected], but submission through Blackboard is preferred.] 2) No late submission is allowed. 3) This is an INDIVIDUAL assignment. Each student should submit one report. 4) Please observe the university’s plagiarism guidelines. Introduction In the first part of this assignment, we analyze the risk of a trading portfolio, and make use of historical prices of some stocks to test the delta hedging strategy. These tests may not be too realistic as some trading conditions have been ignored. In particular, board lots, dividends and transaction costs are not included, but our aim is to show the validity of the theoretical framework. Part two examines some theoretical relationships of derivative trading strategies and product pricing. 2 Part I: Risk Management of a Straddle Position (66%) 1. Choose the stock that you have to work on For this part, your student number decides which stock you have to use to perform the analysis. Take the last two digits of your student number, use modulo 50 to obtain the order number, and look up the stock code from the given data sheet. For example, if your student number ends with 18, the order number is (18 mod 50 = 18), and the stock is Techtronic Industries Co. Ltd. (stock code 669). If your student number ends with 84, the order number is (84 mod 50 = 34), and the stock is BYD Co. Ltd. (stock code 1211). This stock is known as stock X in the questions below. 2. Option pricing (8%) With the implied volatility given in the spreadsheet, use the Black-Scholes equations to price a straddle for stock X, as of December 31, 2020: 1 European call option + 1 European put option, both at the same strike equal to the stock price as of December 31, 2020, continuously compounded interest rate = 0.65%p.a., maturity = 1 year (December 31, 2021), dividend yield = 0. Calculate the total price for this option straddle, with N call options and N put options. 3. Value-at-risk of the straddle (28%) i) Assume that you are short N call options on X and N put options on X as described in (2) above. Denote VaR_95 as the 5-day, 95% confidence interval Value-at-risk for this strategy. Using a procedure similar to the one described in Lecture 9, slide 44 and using the model as in Lecture 6, slide 40, calculate VaR_95 with a Monte Carlo simulation with 500,000 runs. [with t = 5/365] ii) Denote CVaR_95 as the conditional-VaR at 95% confidence interval, which is given as the average of the changes in the portfolio values when the changes exceed VaR_95. Calculate CVaR_95 using the simulation results from 3(i) above. 3 4. Test of delta hedging strategy (30%) i) Assume that you are short N call options on X and N put options on X as described in (2) above. Using the daily price data given in the spreadsheet, construct a delta hedging strategy for the position for the period between December 31, 2020 to December 31, 2021, so that the overall position is delta neutral daily (the format is given in the spreadsheet). The account balance on each day is calculated by summing the following components: Previous account balance. If the account balance is negative, interest has to be paid; if the account balance is positive, interest will be received. The interest is calculated daily, so that the total amount = previou
s day amount balance x exp(interest_rate x num_days/365), where num_days is the number of days from the previous date to the current date, so it can be one day or more than one day, depending on whether there are holidays. Cash required / received from share transaction. Use the given implied volatility to generate the deltas. In your report, include a few lines of this table (but no need to include all the dates). On maturity date, either the call or the put would be exercised. The number of shares in the share account must be equal to +N or N, and this position is to be sold to or bought back from the option holder at the strike price. Denote Fi as the final account balance after taking into account of the above transactions. Find Fi. ii) On December 31, 2020, you have deposited the money that you received from shorting N call options and N put options (as in 2(ii) above) into a deposit account, earning a continuously compounded interest of 0.65% p.a. The maturity of the deposit is December 31, 2021, and the total amount received is Pi. Find Pi. Compare Pi with Fi obtained in 4(i) above (noting that one is positive and the other is negative). Does the final account balance Fi match the corresponding total amount in the deposit account Pi Comment briefly on the result. Note: – delta for a European call option with no dividend: N(d1). Delta for a European put option with no dividend: N(d1) – 1. The total delta for a combination of 1 European call option and 1 European put option = 2N(d1) – 1. – N refer to the “Number of options traded” field as given in the spreadsheet for the relevant stock. 4 Part II: Problem sets (34%) 1. Arbitrage opportunities (24%) In each situation below, identify an arbitrage opportunity, suggest trades to be carried out and calculate the theoretical profit. You should explain how the profit can be realized under different market conditions. Assume transaction costs are 0. (a) FX market (10%) Spot FX level: EUR 1 = USD 1.1345 6-month forward FX rate: EUR 1 = USD 1.1113 EUR 6-month interest rate: 2.15% p.a. USD 6-month interest rate: 1.33% p.a. Assume 6 months = 0.5 year and interest is calculated by the convention rt+1 . (b) Equity options (14%) Current stock price S0: $100 Option maturity T: 0.5 year Interest rate r: 2.75% p.a. (erT=1.01384, e rT=0.98634) Dividend before option maturity: 0 Price of call option today C0: $9.69 Price of put option today P0: $6.30 Strike of the call and put options K: $98.5 2. Equity Linked Investment (10%) An investor has bought a capital guaranteed note (CGN) from a bank based on the Hang Seng index. Some characteristics of the note are: Notional amount: $500,000 Initial note price: 100% of notional amount Tenor: 5 years Reference price S: Hang Seng Index (HSI) Payoff at maturity: 100%+ ×( 0, 0)/0 On trade date, Hang Seng Index S0 = 20134, 5-year interest rate is 1.94% p.a. (annually compounded rate, calculated as (1+r)t), option price is 13.80%, participation rate p is 55%. i. Calculate the commission rate charged by the bank initially. ii. After 2 years (i.e. remaining time to maturity = 3 years), Hang Seng index has already moved up substantially. The mark-to-market option price becomes 41.3%, and the 3- year interest rate becomes 1.45% p.a. The bank would charge a commission rate of 1.20% for an early termination of the CGN. What is the amount that the investor could receive if he decides to terminate this trade and redeem the note What is the equivalent annualized return for the investor iii. If the investor has not terminated the note early and holds the position until maturity, the level of HSI = ST = 27659. No commission is charged at the final redemption. Calculate the equivalent annualized return for the investor. – END –