Task 1

A short forward contract for 10 units of underlying asset (that is notional = -10) and with delivery in six months was entered into at a forward price of 100 USD. Assume that two months later a new forward contract with the same delivery date has a forward price of 110 USD. The riskless rate in the economy is 12% p.a. (continuous compounding). What is the market value of the initial forward contract two months after the deal?

• Note: for continuous discounting you can use the exp function from the numpy library

  • import numpy as np
  • np.exp()
  • program function in general terms
  • return your answer as a scalar

• Note: treat all inputs in the function below as variables subject to testing

Task 4

You observe the following economic conditions: The annual interest rates (compounded continuously) on U.K. and German deposits are 8% and 6% respectively. The current exchange rate is 1.5 EUR per 1 GBP and the forward foreign exchange rate for delivery one year from now is 1.46 EUR per 1 GBP. You desperately need to earn 8 million EUR one year from now for your capital investment, and somebody just told you there might be an arbitrage opportunity on the markets that might allow you to make this money in a riskless way.

• Assuming the interest rates and the current exchange rate given above are correct, what should be the futures price of 1 GBP in EUR according to the interest rate parity? Compute the forward level.

• You realize that given the above data, you (probably) can benefit from an arbitrage opportunity that would allow you to raise the necessary capital at no cost. Describe the necessary actions (and associated cash flows) you need to take now and in one year in order earn 8.0 millions EUR in one year at no cost. Write a function that checks for the existence of covered interest arbitrage and in case of its existence calculates the necessary FX position to produce the required arbitrage profit.

• Note: treat all inputs in the function below as variables subject to testing

• Follow the definitions of the variables in the function description