Question

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.

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 ex-
change rate European put (in EUR).

Answer 1

With the limitation of solving first four subparts let us proceed ahead though the underlying concept remains the same, we just need to replace the value.

a) Local currency GBP

i)  Risk Neutral Probability for the up movement = [(1+ r)-d]/(u-d)= [(1+0.0150)-0.87]/(1.15-0.87)= 0.5179=51.79

For construction of the binomial tree and solution for other questions please refer the image attached for better conceptual clarity.