index future contract involves buying and selling the stock index for a specified price at a specified date. How much will a contract price be if it involves the S&P SmallCap index with a current value of P200 times the index for 1700
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- Put–Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option?An index level of 1,000, what is the value of each contract? If a long stock index futures position on S& P 500 index futures at 1, 051 and has an index of 1, 058 at the settlement date, how much would be the trader’s gain? Complete Solution.The one-year futures price on a particular stock - index portfolio is 1,124.91, the stock index currently is 1, 116, the one-year risk-free interest rate is 2.61%, and the year-end dividend that will be paid on a $1,116 investment in the index portfolio is $13.73. By how much is the contract mispriced? future price - parity price
- You find the following information in December 2019. Assume the T-bill maturity and futures delivery are on the same day. Ignore transactions costs. Treasury Bill Maturity DTM Bid Asked Mar 20 90 1.19 1.18 Index Futures S&P 500 Index (CME) – 250 x index, cents per unit Open High Low Settle Mar 20 3324 3326 3320 3322 S&P 500 closed at $3329 on the same day. Suppose that if you buy one unit of S&P 500 index today, you will be entitled to a 2% dividend yield in March. Design a zero net investment arbitrage strategy involving: (1) buying the index for $3329, (2) shorting the futures for no cash now, (3) and borrowing $3329 at the spot rate. Show your profit per one futures contract (250 units of the index). a. $12,395 b. $10,114 c. $18,948 d. $11,639Consider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 1,950, and the June maturity contract is at F0 = 1,951.a. If the current interest rate is 2.5%, and the average dividend rate of the stocks in the index is 1.9%, what fraction of the proceeds of stock short sales would need to be available to you to earn arbitrage profits?b. Suppose now that you in fact have access to 90% of the proceeds from a short sale. What is the lower bound on the futures price that rules out arbitrage opportunities?c. By how much does the actual futures price fall below the no-arbitrage bound?d. Formulate the appropriate arbitrage strategy, and calculate the profits to that strategy.On January 1, you sold one April S&P 500 index futures contract at a futures price of 1775. If the April futures price is 1918 on February 1, what is your profit or loss if you close your position? The multiplier for the S&P 500 index futures contract is 250. Group of answer choices +35,750 +53,096 +32,933 -32,933 -35,750
- The multiplier for a futures contract on a stock market index is $50. The maturity of the contract is 1 year, the current level of the index is 1,800, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Suppose that after 1 month, the stock index is at 1,820.a. Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly.b. Find the holding-period return if the initial margin on the contract is $5,000Using put-call parity formula, derive expressions for the lower bounds for European call and put options. What is a lower bound for the price of (i) a three-month call option on a non-dividend-paying stock when the stock price is R860, the strike price is R760, and the risk-free interest rate is 10% per annum? (ii) a three-month European put option on a non-dividend-paying stock when the stock price is R500, the strike price is R610, and the discrete risk-free interest rate is 9% per annum?Suppose you buy one SPX call option contract with a strike of 2200. At maturity, the S&P 500 index is at 2218. What is your net gain or loss if the premium you paid was $14? (Input the amount as a positive value.)
- The common stock of Company XLT and its derivative securities currently trade in the market at the following prices and contract terms: Price ($) Exercise Price ($) Stock XLT $ 21.50 $ - Call Option on Stock XLT $ 5.50 $ 21.00 Put Option on Stock XLT $ 4.50 $ 21.00 Both of these options will expire 91 days from now, and the annualized yield for the 91-day Treasury bill is 3.0 percent. a. Briefly explain how to construct a synthetic Treasury bill position. b. Calculate the annualized yield for the synthetic Treasury bill in part (a) using the market price data provided. c. Describe the arbitrage strategy implied by the difference in yields for the actual and synthetic T-bill positions. Show the net, riskless cash flow you could generate assuming a transaction involving 21 actual T-bills and 100 synthetic T-bills. d. What is the net cash flow of this arbitrage strategy at the option…On a particular day, the September S&P 500 stock index futures was priced at 960.50. The S&P 500 index was at 956.49. The contract expires 73 days later. Assuming continuous compounding, suppose the risk-free rate is 5.96 percent and the dividend yield on the index is 2.75 percent. Is the futures overpriced or underpriced? Assuming annual compounding, suppose the risk-free rate is 5.96 percent and the future value of dividends on the index is $5.27. Is the futures overpriced or underpriced?You placed $120,000 in your future trading account have just bought your first HSI June 2023 futures contract today @ 19,652, at market close the HSI June 2023 future closed at 19,534. Currently the initial margin for HSI is $101,944, the maintenance margin is $81,555. HSI futures is $50 per index point. What is you margin account balance as of market closed today? Please write out the detailed calculation steps
