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- The futures price of a commodity is $45. The volatility of the futures price is 14% and the continuously compounded risk free rate is 3% for all maturities. An American put option on the futures contract has strike price of $45 and a time to expiration of 6 months. a. $1.5625 b. $1.5508 c. $0.0The futures price of a commodity is $88. Use a three-step tree to value (a) a nine-month American call option with strike price $91 and (b) a nine-month American put option with strike price $91. The volatility is 28% and the risk-free rate (all maturities) is 3% with continuous compounding. 8.044 and 10.988 7.218 and 10.169 7.734 and 10.679 8.560 and 11.506Suppose the 6-month Mini S&P 500 futures price is 1,345.99, while the cash price is 1,335.81. What is the implied difference between the risk-free interest rate and the dividend yield on the S&P 500? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Implied difference %
- Suppose the 6-month Mini S&P 500 futures price is 1,170.78, while the cash price is 1,158.57. What is the implied difference between the risk-free interest rate and the dividend yield on the S&P 500? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Implied difference %You use a forward binominal tree to price options on a futures contract. You are given: i) The period is 1 year ii) The volatility of the futures price is 30% iii) The initial futures price is 100 iv) The continuously compounded risk-free rate is 3% Calculate the price of a one-year 110-strike European call option on the futures contract. A. 8.68 B 9.13 C 10.32 D 11.54 E 12.06Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean? Explain what is meant by basis risk when futures contracts are used for hedging.
- A Eurodollar futures price changes from 99.45 to 94.32. What is the gain or loss to an investor who is long 5 contracts? Choose the right answer: a. The investor makes gain – 128.25$ b. The investor makes loss – 641.25$ c. The investor makes loss – 195$ d. The investor makes gain – 195.25$ e. The investor makes loss – 128.25$Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Using the Black-Scholes-Merton model, compute the price of a put option on the underlying asset.Assume that the price of a forward contract is 127.87. The European options on the forward contract has an exercise price $150, expiring in 60 days. 3.75% is the continuously compounded risk-free rate, and volatility is 0.33. Calculate the underlying asset's price. Using the Black-Scholes-Merton model, determine the price of a call option on the underlying asset.
- Suppose the standard deviation of monthly changes in the price of a commodity is 0.4. The standard deviation of monthly changes in futures price for a contract on commodity B (similar to commodity A) is 0.5. The correlation between the futures and commodity price is 0.88. What is the hedge ratio and the optimal number of contracts if the commodity trader wants to hedge 10000 bushels and one contract is on 100bushels? Hedge ratio should be rounded off to three decimal places and optima number of contracts should be in whole numbers.Today is September 1. A futures contract on crude oil expiring on December 20 of the same year has a futures price of $44.70. The volatility on the futures contract is 23%, and the continuously compounded risk-free rate is 2%. Assume that there are 365 days in a year. a. What is the Black model price of a European call option on this futures contract, expiring on December 20 and with an exercise price of $46? b. What is the Black model price of a European put option on this futures contract, expiring on December 20 and with an exercise price of $50?Suppose the 180-day futures price on gold is $110.00 per ounce and the volatility is 20.0%. Assume interest rates are 3.5%. What is the price of a $120 strike call futures option that expires in 180 days? Answer to 2 decimal places. Answer: 2.58 to 2.60