Reference no: EM131850114

Consider a currency option for the British pound. The option expires in one year and has the following parameters. Contract amount of British pounds £10 million, strike price $1.200 per £1, annual standard deviation 14.0%, US risk-free rate .45%, UK risk-free rate .46%, spot exchange rate $1.280 per £1. (i) Use Black-Scholes to price this option (calculate the premium) if it is a European call option. (ii) Use put-call parity to price the equivalent put option. (Note, the formula I gave in class was for an asset with no dividend/income yield. This is not so in this case. Therefore, the first thing you need to do is derive the relationship using an arbitrage argument as I did in class. Of course, you can probably find the formula online, but where is the fun in that!) (iii) Suppose that immediately after calculating the values in (i) and (ii) the Bank of England cuts UK interest rates by 20bp meaning that the UK risk-free rate declines to .26%. Repeat the calculations for the call and put options in (i) and (ii). (iv) Suppose you create a portfolio in which you go long one call option and short one put option. Create a profit diagram for this portfolio at expiration including the premiums paid. For this diagram you may use the UK risk free rate of .26%. (v) Does this diagram resemble the payoff diagram for another type of derivative, and if so, what can you say about the characteristics (or parameters) of this other derivative.