Question

1. Currently, 1 Euro is equivalent to 0.88 GBP (i.e., British pounds). Assume that the interest rate over one (annual) timestep in Britain is rGB = 3.5%, and in Europe, it is rE = 2.0%. Operate in CRR notation with u = 1.1, and d = 1/u throughout this question, and be careful to 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).

Answer 1

Solution:

We will be calculating the risk neutral probability using the respective formula and then drawing the 4step binomial tree using GBP as the base currency or the domestic currency. Please refer the below images for the same.

4) As we can clearly see in the binomial tree that in both the upmove as well as the down move the value of the ex rate is greater then 1. So a put option with a strike of 1 will always be Out of the money and will have a zero payoff as well as zero value.