Suppose you pay 10 to buy a European (K=100, t=2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is 110.
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Suppose you pay 10 to buy a European (K=100, t=2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your
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- Suppose you pay 10 to buy a European (K = 100, t = 2) call option on a given security. Assuming a continuously compounded nominal annual interest rate of 6 percent, find the present value of your return from this investment if the price of the security at time 2 is (a) 110; (b) 98.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?
- Consider a 2-year EUROPEAN PUT with a strike price of $65 on a stock whose current stock price is $60. Suppose that there are two time steps, and in each time step the stock price either moves up by 20% or moves down by 20%. Also suppose that risk-free rate is 5% per annum with continuous compounding . What is the value of the European put option?What is the risk-neutral valuation of a six-month Euro-pean put option to sell a security for a price of 100 when the current priceis 105, the interest rate is 10%, and the volatility of the security is .30?An investor buys a ($1000 FV) Treasury Strip security with 11 years to maturity at a yield of 5.1%. Two years later the yield to maturity on the strip is 4.0% and the investor decides to sell. What is the compounded annual rate of return on the investment over the investment horizon? For simplicity assume all yields in the question are quoted with annual compounding. Enter your answer as percent to two decimal places, but do not include the % sign.
- Suppose that a risk-free investment will make three future payments of $100 in one year, $100 in two years, and $100 in three years. If the Federal Reserve has set the risk-free interest rate at 8 percent, what is the proper current price of this investment? What if the Federal Reserve raises the riskfree interest rate to 10 percent?You are considering an investment in a 40-year security. The security will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The nominal interest rate is assumed to be 8%, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (for 17 years)?What is the present value for a future value of FV=$500,000 at time t=36 if the interest rate is r=0.05 (e.g., r=5%)? What is the interest rate “r” if PV=$100 and the FV=$350 in year t=12? What is the interest rate “r” if PV=$1250 and the FV=$2150 in year t=10? How long will it take to double your investment if the interest rate is r=0.06 (r=6%)? How long will it take to increase your investment by 2.5 times if the interest rate is r=0.14 (r=14%)? Which is the better option if the interest rate is r=0.10 (r=10%)? Show all work used to arrive at your answer. a. Option I: Receive $1000 today at time t=0. b. Option II: Receive $1615 at time t=5.10) Which is the better option if the interest rate is r=0.07 (r=7%)? Show all work used to arrive at your answer. a. Option I: Receive $510 today at time t=0. b. Option II: Receive $1000 at time t=10.
- A European-style put option that expires two periods from now has an exercise price of $125. The per-period risk-free rate in the economy is 5.4%. The underlying asset currently sells for $107.50 and will either go up in value by 12% or down by 10%. How much should the put option sell for right now? Round your answer to the nearest penny.According to the concepts underlying the present-value formula, would you prefer to receive (a) P75 one year from now, (b) P85 two years from now, or (c) P90 three years from now, if the relevant market interest rate is 10% and will remain at 10% for the next three years? a. The present values of all three choices are identical b. P75 one year from now c. P85 two years from now d. P90 three years from nowYou are considering the choice between investing £50,000 in a conventional 1-year financial asset such as (Certificate of Deposit) offering an interest rate of 5% and a 1-year “InflationPlus” offering 1.5% per year plus the rate of inflation. (a) Which is the safer investment and why? Which offers the higher expected return and why? If you expect the rate of inflation to be 3% over the next year, which is the better investment? Explain. If we observe a risk-free real rate of 5% per year and a risk-free real rate of 1.5% on inflation indexed bonds, can we infer that the market’s expected rate of inflation is 3.5% per year?
