Options and Futures (BusFin 4229) Spring 2024 Problem Set #3: Forward - Futures Pricing / Futures Trading / Mark-to- Market Process / Option Pricing This problem set is due on Wednesday, March 27th, 2024, via Carmen until 11:59 pm. Please DO NOT send me a copy via email. Submit one copy per group. Question 1 (7 points) Suppose today S&P 500 index is 1800 and the continuously compounded annual dividend yield on the index is 2%. Assume that it is possible to lend at 4 % and borrow at 7 %, annually continuously compounded. a) Above what futures price is there arbitrage? b) Below what futures price is there arbitrage? Please show the cash flows, which make each type of arbitrage and explain what you would do at each relevant date. Consider time to maturity of 6 months. Question 2 (8 points) Suppose call prices are given by StrikePrice($) Call Premium($) 10 20 30 542 What no arbitrage property is violated? What spread position would you use to effect arbitrage? Demonstrate that spread position is an arbitrage by creating a table, which shows possible profit opportunities at the time to maturity. Assume option's time to maturity is 1 year and continuously compounded interest rate is 4%. Question 4 (10 points) Suppose an investor has a 2 LONG Gold Futures position on June 7th, 2023. Current gold futures price is $900 per ounce of gold. At the end of each trading day, the margin account is adjusted to reflect the investor's gain or loss, daily settlement, marking to market. Initial Margin is $2,000 per contract. Maintenance margin is $1,500 per contract. Contract size is 100 ounces. If the investor decided to close out on June 29, 2023, at $892.30, what will be his/her margin account balance? (Ignore interest rate calculations, r=0%). Fill in the blanks in the following table. Day Futures Price ($) Change in Daily Gain (Loss)($) Cumulative Gain Margin MARGIN Account Call ($) Futures (Loss)($) Balance Price ($) ($) June 7 900.00 June 8 897.00 June 9 896.10 June 10 898.20 June 11 897.10 June 14 896.70 June 15 895.40 June 16 893.30 June 17 893.60 June 18 891.80 June 21 892.70 June 22 887.00 June 23 887.00 June 24 888.10 June 25 888.70 June 28 891.00 June 29 892.30 +