You wish to price a call option on the GBP, with the following details:

Spot exchange rate: 1.25 USD per GBP

Strike price: 1.30 USD per GBP

USD interest rate: 2.00%

GBP interest rate: 0.25%

Volatility: 10%

Time to maturity: 1 year

Notional amount: 100 GBP

Please provide the option premium and the options delta.

b. We are now going to examine small changes in the parameters that affect the option premium. For each of the changes suggested below, please provide the new options premium, and state whether the premium has increased or decreased relative to the value you calculated in part (a).

Change #1. Use the parameters in (a) above. Then increase the spot exchange rate to 1.45 USD per GBP.

Change #2. Use the parameters in (a) above. Then increase the strike price to 1.45 USD per GBP.

Change #3. Use the parameters in (a) above. Then decrease the time to maturity to 3 months.

Change #4. Use the parameters in (a) above. Then increase the volatility to 15%.

c. Please:

(i) estimate the delta of the call option above.

(ii) If you were a market maker and had sold the call option above to a client, do you have an implicit long or short position in the GBP? How would you hedge this exposure?

d. You price the call option described in Part (a), but to your surprise, you observe several different prices for the exact same option in the market.

(i) You observe a price of USD2.50 for the option. What is the implied volatility that corresponds to this price?

(i) You observe a price of USD7.50 for the option. What is the implied volatility that corresponds to this price?