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Futures price of a commodity is currently trading at 100. By delivery date, futures price can either rise to 140 or drop to 70. The put option has K =90. To create a hedge portfolio with one put and some futures, we need to ______ futures contract for one put option we long.
- A. short .25
- B. short .35
- C. short .28
- D. long .35
- E. long .28
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- In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1) What assumptions underlie the OPM? (2) Write out the three equations that constitute the model. (3) According to the OPM, what is the value of a call option with the following characteristics? Stock price = 27.00 Strike price = 25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49Find the price of an American call option on a futures if the current spot price is 30, the exercise price is 25, the futures price is 33.70, the risk-free interest rate is 6 percent, the spot asset can go up by 10 percent or down by 8 percent per period and the call expires in two periods, which is also when the futures expires. Show your working. A. 9.98 B. 8.70 C. 7.73 D. 8.22Suppose 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.
- 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.The S&P 500 futures price is 4372 and you have a portfolio of stocks valued at $20,000,000. Each futures contract is worth $250. If the portfolio moves exactly like the index, how many contracts do you need to hedge this portfolio and what is the implied beta?A trader buys (long) a call option with a strike price of $120 andsells (short) a put option with a strike price of $100. Both options have the same maturity.The call costs $20 and the price of put is $10. What is the portfolio payoff at expiry ifthe security price at expiry is $70? Draw a diagram showing the variation of the trader’sprofit with the security price at expiry.
- 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 12.06Consider a portfolio consisting of 6 stocks and 10 put options on the stocks. The current stock price is S0 = 100 and the stike price of the options is X = 100. The stock pricecan take on only two values at maturity T given by Su = 120 and Sd = 90. The risk-free rate is given by 5%. (1) How many put options with strike price X = 110 are necessary in the portfolio to have a certain payoff at maturity?(2) Find the value of a put option P0 with strike price X = 100.(3) Find the value of a call option C0 with X = 100 by using the Put-Call-Parity. Verify that your answer by calculating the price C0 directly.Demonstrate how a Margin Account operates for both the Long and the Short futures position using the following information: The initial margin is R30. The initial Futures price is R100. On Day 1 the price drops to R90. On Day 2 the price rises to R95.
- The futures price of a commodity such as wheat is $2.50 a bushel. Futures contracts are for 10,000 bushels, and the margin requirement is $2,500 a contract. The maintenance market requirement is $1,000. A speculator expects the price of the commodity to rise and enters into a contract to buy wheat. a. How much must the speculator initially remit? b. If the futures price rises to $2.60, what is the profit and return on the position? c. If the futures price declines to $2.47, what is the loss on the position?In a financial market a stock is traded with a current price of 50. Next period the priceof the stock can either go up with 30 per cent or go down with 25 per cent. Risk-freedebt is available with an interest rate of 8 per cent. Also traded are European optionson the stock with an exercise price of 45 and a time to maturity of 1, i.e. they maturenext period.a) Find prices of Arrow-Debreu securities.b) Calculate the price of a call option by constructing and pricing areplicating portfolio.A Futures price is currently €80. Over each of the next two 3 month periods it will rise or fall by 10%. The risk free rate is 8% p.a. (i)Using replicating portfolio techniques, find the value of a 6 month European call option on the futures with strike €80. (ii)Verify your answer using risk-neutral valuation. (iii) Would your answer change if the call was American? is this question valued as a future or a call option ? As in which Formula
