Reference no: EM132626951

At writing, 1 Euro is equivalent to 0.89 GBP (i.e., British pounds).

Assume that the interest rate over one (annual) timestep in Britain is rGB = 1.5%, and in Europe, it is rE = 2.0%. Operate in CRR notation with u = 1.15, and d = 1/u throughout this question, and specify which currency you are using in all answers.

(a) Assume that your domestic currency is GBP.

(i) Calculate the risk neutral probability for an exchange rate option. Let each time step represent one year, so you can use the interest rates given without conversion.

(ii) Construct a 4-step binomial tree for the exchange rate.

(iii) Assume the strike rate of an exchange rate (European) call option is k = 1.00 GBP/EUR, and the face value is F = EUR10, 000. Construct a binomial tree and calculate the premium of this call option, in GBP.

(iv) Using the same strike rate and face value, calculate the premium of an exchange rate European put (in GBP).

(b) Now, instead assume your domestic currency is Euros.

(i) Calculate the risk neutral probability for an exchange rate option. Let each time step represent one year, so you can use the interest rates given without conversion.

(ii) Construct a 4-step binomial tree for the exchange rate.

(iii) Assume the strike rate of an exchange rate (European) call option is k = 1.00 EUR/GBP, and the face value is F = GBP10, 000. Construct a binomial tree and calculate the premium of this call option, in EUR.

(iv) Using the same strike rate and face value, calculate the premium of an exchange rate European put (in EUR).

(c) Compare the premiums from parts (a) and (b): what do you observe? It may help to convert them into the same currency.