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.)
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- Work out the value of European Call on a risky asset A, currently selling at $600. The European Call has a term to maturity of 1.5 years and a strike price of $675. SD(dA/A), the volatility of returns on the risky asset is 18% per year, and the discrete risk-free rate is 0.9% per yearAn asset has a current price of $10 and has volatility of 0.35. The exercise price in 9 months is $13. The US continuous risk free rate (r^f ) is 5.5% while the Philippine continuous risk-free rate (r^d ) is 6.5%. The value of the call option and put option would be?On the London Metals Exchange, the price for copper to be delivered in one year is $5,820 a ton. (Note: Payment is made when the copper is delivered.) The risk-free interest rate is 2.00% and the expected market return is 8%. a. Suppose that you expect to produce and sell 10,000 tons of copper next year. What is the PV of this output? Assume that the sale occurs at the end of the year. (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.) b-1. If copper has a beta of 1.28, what is the expected price of copper at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b-2. Assume copper has a beta of 1.28. What is the certainty-equivalent end-of-year price?
- You buy a European put option priced at $0.025/€ on €225,000 at a strike price of $1.50/€. If at maturity, the observed price is $1.60/€, what is the total net cash flow involved at the end of this investment whether you exercise or do not exercise this option?The British pound (£) is currently worth 1.45 euros (€). This can either increase by u = 1.1 or decrease by d = 0.9 over each 4 months. Consider a European call option with a strike price of K = 1€ per £ and time-to-maturity T = 8 months. The continuously compounded risk-free rate in Britain is 4% per annum and in Europe is 10% per annum. What is the price of the European call option today? Please explain your answer using your own words and show your workings. In addition, if the option was American-style would the risk-neutral probability of an up-move be smaller than, equal to or greater than the one you have calculated? Explain why using your own words.The British pound (£) is currently worth 1.45 euros (€). This can either increase by u = 1.1 or decrease by d = 0.9 over each 4 months. Consider a European call option with a strike price of K = 1€ per £ and time-to-maturity T = 8 months. The continuously compounded risk-free rate in Britain is 4% per annum and in Europe is 10% per annum. What is the price of the European call option today? Please explain your answer using your own words and show your workings. In addition, if the option was American-style would the risk-neutral probability of an up-move be smaller than, equal to or greater than the one you have calculated?
- Q1 A long forward contract on a commodity that was negotiated some time ago will expire in 1 months and has a delivery price of $70. The current spot price of the commodity is $59. The risk-free interest rate (with continuous compounding) is 0.09. What is the value of the long forward contract? Q2 A short forward contract on an investment asset that yields 0.08 and was negotiated some time ago will expire in 4 months and has a delivery price of $50. The current spot price of the commodity is $48. The risk-free interest rate (with continuous compounding) is 0.02. What is the value of the short forward contract? Q3 A long forward contract on a commodity that was negotiated some time ago will expire in 2 months and has a delivery price of $76. The current spot price of the commodity is $66. The risk-free interest rate (with continuous compounding) is 2.2%. What is the value of the long forward contract?You buy a European call option priced at $0.025/€ on €225,000 at a strike price of $1.50/€. If at maturity, the observed price is $1.60/€, what is the total net cash flow involved at the end of this investment whether you exercise or do not exercise this option?A short forward contract on an investment asset that yields 7.2% and was negotiated some time ago will expire in 10 months and has a delivery price of $68. The current spot price of the commodity is $48. The risk-free interest rate (with continuous compounding) is 3.5%. What is the value of the short forward contract
- 1. Suppose a financial asset, ABC, is the underlying asset for a futures contract with settlement of 6 months from now. You know the following about this financial asset and futures contract in the cash market ABC is selling for $80; ABC pays $8 per year in two semiannual payments of $4, and the next semiannual payment is due exactly 6 months from now; and the current 6month interest rate at which funds can be loaned or borrowed is 6%. a) Compute for the profit for the transaction? b) What is the theoretical (or equilibrium) futures price? c) What action would you take if the futures price is $837 d) What action would you take if the futures price is $76? SHOW SOLUTIONS PLEASE DONT USE MSEXCELConsider a one-period binomial model in which the underlying is at 65 Euros, and can go up 30% or down 22% each period. The risk-free rate is 8%. European Put Option with Execution Price of 70 Euros. Assume that the put is selling for 9 Euros. Demonstrate how to execute an arbitrage transaction and calculate the rate of return. Use 10000 puts.Suppose a world has two risky assets: StkC and StkD. The following table shows the holding period returns in each scenario. Suppose the T-bill rate is 3%. Scenario Probability Return for StkC Return for StkD Severe recession 0.03 -40% -12% Mild Recession 0.02 -10% 10% Normal 0.9 10% 6% Mild growth 0.02 20% 8% Boom 0.03 60% -20% Which answer is the closest value to the fifth-percentile value at risk (VaR) of holding StkC? -40% -10% 10% 20% 60%