9. Suppose four-period ATM European lookback on maximum strike put option, whose underlying stock price of $100 with a degree of up and down movements of 20% and 10% for each year respectively. The risk-free annual rate is 5%.
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- 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 six-month European call option on the spot price of gold, that is, an option to buy oneounce of gold in the spot market in six months. The strike price is $1, 200, the six-month futuresprice of gold is $1, 240, the risk-free rate of interest is 5% per annum, and the volatility of thefutures price is 20%. The option is the same as a six-month European option on the six-monthfutures price. Calculate the value of this option.
- 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.Consider a European call option on the S&P 500 that is two months from maturity. The currentvalue of the index is 930, the exercise price is 900, the risk-free interest rate is 8% per annum,and the volatility of the index is 20% per annum. Dividend yields of 0.2% and 0.3% are expectedin the first month and the second month, respectively. Calculate the call priceConsider 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?
- A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put–call parity.The stock price is currently $100. Over each of the next two six-month periods, it is expected to go up by 20% or down by 20%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a one-year European call option with a strike price of $100? What is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call parity.A futures price is currently 65, its volatility is 22% per annum, and the risk-free interest rate is 5.5% per annum. What is the value of a five-month European put on the futures with a strike price of 60?
- A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European put option with a strike price of $95. The risk-free interest rate is 8% per annum, compounded continuously. What is the value of the option if it is American?The current price of YBM stock S is $55. At-the-money European options with a strike price K = S and maturing in T = 6 months trade on YBM. The continuously compounded, risk-free interest rate r is 1.8 percent per year. If the call price is $5.22, then the no-arbitrage put price isThe real risk-free rate is 3.25%, and inflation is expected to be 3.75% for the next 2 years. A 2-year Treasury security yields 9.25%. What is the maturity risk premium for the 2-year security? Round your answer to two decimal places.