What is the value of a derivative that pays off $100 in six months if an index is greater than 1,000 and zero otherwise? Assume that the current level of the index is 960, the risk-free rate is 8% per annum, the dividend yield on the index is 3% per annum, and the volatility of the index is 20%.
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What is the value of a derivative that pays off $100 in six months if an index is greater than 1,000 and zero otherwise? Assume that the current level of the index is 960, the risk-free rate is 8% per annum, the dividend yield on the index is 3% per annum, and the volatility of the index is 20%.
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- What is the value of a derivative that pays off $300 in 6 months if an index is less than 900 and zero otherwise? Assume that the current level of the index is 920, the risk - free rate is 8% per annum, the dividend yield on the index is 3% per annum, and the volatility of the index is 20%. 1. 95.33 2. 68.71 3. There is no correct answer. 4. 41.08 5. 114.39Answer the following question and give the specific process: What is the value of a derivative that pays off $100 in six months if an index is greater than 1,000 and zero otherwise? Assume that the current level of the index is 960, the risk-free rate is 8% per annum, the dividend yield on the index is 3% per annum, and the volatility of the index is 20%. (Hint: Use Binary options)Suppose that the risk-free interest rate is 6% per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create?
- The stock price is currently $30. Each month for the next two months it is expected to increase by 8% or reduce by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off [max(30 — St; 0)]2, where St is the stock price in two months? If the derivative is American-style, should it be exercised early?The S&R index spot price is 1100 and the continuously compounded interest rate is 5%. You observed a 9-month forward price of 1129.257. (a) What is the implied dividend yield? (b) Suppose you believe the dividend yield will be 3% over the next 9 months. How can you arbitrage?Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35. The current index level is 2,000. Assume that you can short sell the S&P index.a. Suppose the expected rate of return on the market is 8%. What is the expected level of the index in one year?b. What is the theoretical no-arbitrage price for a 1-year futures contract on the S&P 500 stock index?c. Suppose the actual futures price is 2,012. Is there an arbitrage opportunity here? If so, how would you exploit it?
- Suppose a stock is currently (time t = 0) worth 100. Further, suppose the one year annually compounded interest rate is 2%, and the two year annually compounded rate is 3%. Find the following:a) The forward price for a forward contract on the stock with maturity year T1 = 1. b) The forward price for a forward contract on the stock with maturity year T2 = 2.c) The forward price for a forward contract with maturity T1 = 1 on a ZCB with maturity T2 = 2.d) The forward price for a forward contract with maturity T1 = 1 on a forward contract on the stock with maturity T2 = 2 and delivery price K = 101.A one-year long forward contract on a dividend-paying stock is entered into, when the stock price is $40 and the risk-free rate of interest is 10% per annum with continuous compounding. The dividend yield on the index is 2% per annum with continuous compounding. What are the forward price and the initial value of the forward contract?Assume that the risk free-rate yield curve is flat at 4% (with continuous compounding). The payoff from a derivative occurs in 4 years. It is equal to the 6-year rate minus the 2-year rate at this time, applied to a principal of $10 million with both rates being continuously compounded. Calculate the value of the derivative. Assume that the volatility for all rates is 20%
- The multiplier for a futures contract on a certain stock market index is $250. The maturity of the contract is one year, the current level of the index is 1,500, and the risk-free interest rate is 0.2% per month. The dividend yield on the index is 0.1% per month. Suppose that after one month, the stock index is at 1,533. Find the cash flow from the mark-to-market proceeds on the contract. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Cash flowA stock index currently stands at 100. The risk-free interest rate is 4% per annum (with continuous compounding) and the dividend yield on the index is 2% per annum. What should the futures price for a four-month contract be?12. The S&P 500 is currently at 2888. The CBOE far-term VIX (^vif) is at 13.15, and the one-year LIBOR rate is 2.75%. Assuming that the far-term VIX is the right volatility for one-year options, what is the value of a derivative that pays off $1000 if the S$P 500 is above 2900 one year from today? Assume the dividend yield for the index is 1% per year.