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- Suppose a European call option to buy 1 euro for 1.40 CAD costs 0.08 CAD. The option maturity is in two months and the forward exchange rate for the same maturity is 1.50 CAD per euro. What arbitrage opportunity exists? Explain how you can exploit this opportunity and how much the profit is. (Ignore the time value of money)A put option is written on €100 with a strike price of $1.00 = €1.00. In one period, there are two possibilities: the exchange rate will move up by 15 percent or down by 15 percent (i.e. $1.15 = €1.00 or $0.85 = €1.00). The U.S. risk-free rate is 5 percent over the period. The risk-neutral probability of dollar depreciation is 2/3 and the risk-neutral probability of the dollar strengthening is 1/3. What is the intrinsic value of the total option premium including the consideration of time value of money? $4.76 A. B. C. D. €4.76 €9.52 $9.52The British pound (£) is currently worth 1.45 euros (€). This can either increase by u = 1.1 or decrease by d = 0.9 over each 4 months. Consider a European call option with a strike price of K = 1€ per £ and time-to-maturity T = 8 months. The continuously compounded risk-free rate in Britain is 4% per annum and in Europe is 10% per annum. What is the price of the European call option today? Please explain your answer using your own words and show your workings. In addition, if the option was American-style would the risk-neutral probability of an up-move be smaller than, equal to or greater than the one you have calculated?
- Consider a one period binomial model of a currency option on the dollar. Thecurrent (date t = 0) spot exchange rate is S0 = 75 pence per dollar. The spot rateat the end of the period will be either Su = 100 pence or Sd = 60 pence. The UKrisk-free interest rate over the period is rs = 1/3 (33.3333%) and the US risk-freerate of interest is rd = 1/4 (25%). There is a call option with a strike price ofK = 68 pence and a forward contract with a price of F = 80 pence. Show how touse the forward contract and the UK money market to replicate the payoffs to thecall option and hence, find the price of the call option.The British pound (£) is currently worth 1.45 euros (€). This can either increase by u = 1.1 or decrease by d = 0.9 over each 4 months. Consider a European call option with a strike price of K = 1€ per £ and time-to-maturity T = 8 months. The continuously compounded risk-free rate in Britain is 4% per annum and in Europe is 10% per annum. What is the price of the European call option today? Please explain your answer using your own words and show your workings. In addition, if the option was American-style would the risk-neutral probability of an up-move be smaller than, equal to or greater than the one you have calculated? Explain why using your own words.5. Suppose that the exchange rate is €0.80/$. A 2-year euro-denominated European call option on dollars with a strike of €0.90 sells for €0.10. The continuously compounded risk-free interest rate on euros is 2.5% and the continuously compounded risk-free interest rate on dollars is 2%. Calculate the price of a 2-year euro-denominated European put option on dollars with a strike of C0.90.
- If the spot price is 86.5BDT/US$ and the 3 months European put option exercise price is 87.75BDT/US$. If our interest rate is 9% and U.S. interest rate is 3% and given the volatility σ is 18.1%, what should be the price of this European put option?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.Suppose that the spot price of a Canadian dollar is U.S. $0.89 and that the exchange rate has a volatility of 7% per year. Risk-free interest rates are 6% in the U.S. and 4% in Canada. Calculate the price of a 6-month European call option to buy one Canadian dollar for U.S. $0.89. Express your answer in terms of the cumulative normal distribution function, N(x), as in the answers to question 16 in part 1. What is the price of a 6-month option to buy U.S. $0.89 for one Canadian dollar? Please show all your work! Thank you SO much
- Using the UIP equation, assume that the expected future rate (after one year) for euros (in terms of dollars) equals $1.20, while the current spot rate is 1.15. The current interest rate on euro deposits is 2%, and the interest rate on dollar deposits is 3%. Should you invest in the US or in Europe? Neither one In the US In Europe It is indifferentFind the lower bound of a European foreign currency put if the spot rate is $3.50, the domestic interest rate is 8 percent, the foreign interest rate is 7 percent, the option expires in six months, and the exercise price is $3.75. (The interest rates are continuously compounded.)Consider the following information for an exchange rate: • Current spot rate is USD 1.70 for 1 GBP • Risk-free US rate of interest is 6% p.a. compounded continuously. • Risk-free UK rate of interest is 8% p.a. compounded continuously. • Volatility (o) of the currency returns is 20% p.a. • Maturity of the option is 9 months. • Strike rate of the option is USD 1.50 for 1 GBP • The currency options are European in nature •N How much does it cost to hold (i.e., buy) a call-USD option? Use the Garman Kohlhagen model.
