See attached. I want Shakeel. He completed assignments 75117 and 76124.
This assignment focuses on the basics of futures and options. The futures questions deal with ‘fair’ valuation of futures contracts and how the information from market prices can be used. The first two problems deal with gold futures and foreign exchange futures. The third one deals with index arbitrage. The options questions deal with payoff (profit) diagrams and basic strategies. Though you could answer these problems without knowing the detailed specification of the contracts, in reality when you trade in these markets you must familiarize yourself with the market’s operations and contract specifications. Please submit your assignment in one excel document with a tab for each question providing supporting documentation that show all your backup data, calculations, and formulas. Futures: Q1. Suppose the spot price of gold is $1880 per ounce. The futures price for delivery in six months is $1891, while the futures price for delivery in one year is $1902. The interest rate on 6-month loans is 1.00 percent (on an annual basis, continuous compounding). a. Ignoring transactions costs, does this represent an arbitrage opportunity? Why? b. What is the implied interest rate for the first six months? c. What is the implied forward rate six months hence? (Recall computing forward rates from bonds with different maturities). Is the yield curve upward sloping? d. Suppose the spot price of gold is, instead, $1883 per ounce and the six months futures has not changed (1891). Assuming gold can be sold short at a transactions cost of $2.0 per ounce (paid up front), describe an arbitrage strategy. What are the arbitrage gains, if any? Q2. Suppose the spot price for Euro is $1.25, the futures price for delivery in 6 months is $1.255. Assume that the 6 month borrowing/lending rate in Euro is 0.25 percent (annually, continuous compounding) and the corresponding rate in $ is 0.75 percent (annually, continuous compounding). (This is an FX application using the same cost of carry model). a. Assume no transactions costs, do the above prices represent an arbitrage opportunity? Why? b. What are the implied interest rates in Europe and the U.S.? Q3. Compute the ‘fair’ value of the next two futures contracts (March & June 2021) on the S&P500 Index (SPX) using SPX as the underlying asset (this is an open question, no one specific solution since it depends on the day/time that each of you is using and the rates that you think are relevant). Answer the following questions: a. What interest rate and dividend yield did you use? b. Did the futures contract settle above or below SPX? c. What are the transaction costs in index arbitrage activity? d. What are the implied interest rates using the settlement prices? e. What are the issues in doing index arbitrage (e.g. short selling)? Options: Q1. The first simple exercise that you should try is to draw payoff diagrams (or profit diagrams) of various strategies. Get the web page http://www.cboe.com/DelayedQuote/QuoteTable.aspx for the closing prices of SPY options, or use the quotes on Bloomberg or Yahoo Finance. (Notice; payoffs do not include the option premium (price) while profits include the option premium (price)). Here are a few possible strategies: (additional examples will be presented and discussed in class). a. Buy the near term ATM (at-the-money) straddle. b. Write the near term ATM call spread. c. Buy the near term ATM put spread. d. Write the near term ATM butterfly spread. e. Buy 1 basket (SPX or HSI), Buy 1 near term ATM put f. Buy 1 near term ATM put; Write 1 near term ATM call g. Buy an ATM put spread; Buy an ATM call spread Q2. In each of the following 5 cases, what strategy will assure a profit if options on gold are priced as follows: a. C(K = 1900, T1 = Apr.) > C(K = 1900, T2 = June) b. C(K = 1920, T1 = Apr.) > C(K = 1900, T1 = Apr.) c. C(K = 1900, T1 = Apr.) > C(K = 1920, T2 = June) d. C(K = 1900, T1 = Apr.) < (s="" -="" pv(k))="" e.="" p(k="1900," t1="Apr.)"> C(K = 1900, T1 = Apr.) Q3. The following three call options on gold, all expiring in three months, sell for: Exercise priceOption price $1850 $ 120 $1900 $ 90 $1950 $ 70 Consider the following position: buy 1 call with K = 1850 sell (write) 2 calls with K = 1900 buy 1 call with K = 1950 What would be the values at expiration of such a spread for various prices of spot gold? What investment would be required to establish the spread? Given information about the prices of the $1850 and $1950 options, what could you predict about the price of the $1900 option?