Consider a European put with an exercise (strike) price of 5.00 and with 6 months to maturity. The underlying asset has a volatility of 30% and the riskless rate is 5% per year. Estimate a numerical upper bound for the asset price S(t) (to nearest 0.01) at which an European put will sell below its intrinsic value of max(E-S(t), 0). (Compute P(S, t) and E-S(t) for some values of S(t) below the strike price. Compute P(S, t) to at least 3 decimal places.)

Consider a European put with an exercise (strike) price of 5.00 and with 6 months to maturity. The underlying asset has a volatility of 30% and the riskless rate is 5% per year. Estimate a numerical upper bound for the asset price S(t) (to nearest 0.01) at which an European put will sell below its intrinsic value of max(E-S(t), 0). (Compute P(S, t) and E-S(t) for some values of S(t) below the strike price. Compute P(S, t) to at least 3 decimal places.)

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose that the current rates on 60 and 120 day GICs are 5.50% and 5.75%, respectively. An investor is weighing the alternatives of purchasing a 120 day GIC versus purchasing a 60 day GIC and then reinvesting its maturity value in a second 60 day GIC.What would the interest rate on 60 day GICs have to be 60 days from now for the investor to end up in the same financial position with either alternative?
Suppose that the invester of GMO has an extra cash reserveof $700,000 to invest. The interest rate is 1.49% per year in the United States and 6.47% per year in Mexico. Currently, the spotexchange rate is 19.780 Pesos per dollar and the one-year forwardrate is €19.790 per dollar. The investor does not wishto bear any exchange risk. Assess how he can construct an arbitrage portfolio based on your calculation.
4. Let R be the one-year LIBOR rate with annual compounding that will be determined in 6 years from now. Assume the forward interest rate volatility for the corresponding period is 20% per year. The risk-free rates with annual compounding are currently 5% for all maturities. a. Calculate the price of a financial derivative that pays 1000R € in 6 years from now. b. Calculate the price of a financial derivative that pays 1000R € in 7 years from now.
A) It is now January. The current interest rate is 5% per annum annual compounding. The June future price for gold is $1846.30, while the December future rice is $1860.00. Find a strategy to explore the arbitrage opportunity. B) Suppose that the spot price of the euro is currently $1.5 USD. The one-year futures price is $1.55 USD. Is the interest rate higher in the United States or the euro zone? Justify your answer. C) OneAsx has just introduced a single-stock futures contract on Arandex stock, a company that currently pays no dividends. Each contract calls for delivery of 1,000 shares of stock in one year. The T-bill rate is 6% per year annually compounded and Arandex stock currently sells at $120 per share. If the Arandex price drops by 3%, what will be the change in the future price and the change in the investors’ margin account who has a long position in one contract?
The share price of your favourite company is currently traded at a price of £60 and interest is compounded continuously at rate 3.7% per year. Assume that the share evolves according to a discrete time LogNormal process with time measured in years, drift μ= 0.15 and volatility o = 0.24. You decide to buy a European call option with a strike price of £63 and an expiration date of two years from now. What is the no- arbitrage price for this option? State your answer to the nearest pence. Do not enter the pound sign.
Is there an arbitrage opportunity in this market? Explain.
The spot price of oil is $40 per barrel and the cost of storing a barrel of oil for one year is $3.3, payable at the end of the year. The risk-free interest rate is 2.6% per annum, continuously compounded. What is an upper bound for the one-year futures price of oil? Your answer should be correct to one decimal place. Assume there are no transaction costs involved in arbitraging over-priced futures contracts.
The market price of a security can be modelled by assuming that it will either increase by 25% or decrease by 15% each month, independently of price movement in other months. No dividends are payable in the next two months. The continuously compounded monthly risk-free rate of interest is 1%. The current market price of the security is 127. a.) Use the binomial model to calculate the value of a two-month European put option on the security with strike price of 125. b.) Calculate the value of a two-months American put option on the same security with the same strike price. c.) Calculate the value of a two-months American call option on the same security with the same strike price.
4. An American put option to sell a British pound for dollars has a strike price of $1.5 and a time to maturity of 1 year. The volatility of the pound/dollor exchange rate is 15% per annum, the dollar interest rate is 6%, the British pound interest rate is 7%, per annum, and the current exchange rate is 1.52. Use a three-step binomial tree to value the option.
It is given that dP/dt = rP (r being the annually compounded interest rate and P is the amount in the account at any given time). Suppose that an account earns at an annual rate of r percent compounded continuously and a person is drawing an income of H dollars per year withdrawn continuously (impossible, but a modeling assumption). Use phase line analysis to analyze the behavior of the account. Discuss the meaning of any equilibrium points and their stability. If r = 10% (a reasonable rate for long-term stock investments), and H = $10,000, how long should an initial investment of $50,000 be left untouched so that when withdrawals begin the capital is not depleted?
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