QUESTION 3 (PROFIT AND LOSS ATTRIBUTION COMPUTATION) (a-f: 2 points each; g: 21 points; h: 12 points) This question relates to what we have discussed in class around Taylor's expansion and its application to P\&L attribution. P\&L here means "Profit or Loss". In this question we regard the time effect of a few minutes is negligible in valuation of an one year contract (hence T=1 always). You may not want to round your answer too early because it may affect subsequent computations. If you prefer you may assume no rounding for this question. Sam is a New York based trader and he values everything in USD. Guillaume is a Paris based trader and he values everything in EUR. That is, Sam's numeraire is USD while Guillaume's numeraire is EUR. On March 15, 2014, 9:59 am NY, EUR/USD instantaneous exchange rate is 1 EUR = 1.29 USD; EUR continuous compounding zero rate is 0.5%; USD continuous compounding zero rate is 1%. At 9:59am NY Sam enters into a EUR/USD forward contract with Guillaume, to buy one million EUR and sell USD at strike K equal to forward EUR/USD exchange rate with delivery date Mar 15, 2015. a) Find K. b) What is the value of this contract in USD to Sam at 9:59am NY? c) What is the value of this contract in EUR to Guillaume at 9:59 am NY? At 10:00am NY, market moves. EUR/USD instantaneous exchange rate is now 1EUR=1.30 USD. All other market data remains the same d) What is the P\&L of this trade in USD to Sam at 10:00am NY? e) What is the P\&L of this trade in EUR to Guillaume at 10:00am NY? f) Does this EUR P\&L amount have the same as value as Guillaume's P\&L amount in USD at 10:00am NY? (remember at 10:00am, 1EUR=1.30USD ) At 10:01am NY a crisis hit and the market data has drastically changed: EUR/USD instantaneous exchange rate goes up to 1 EUR =1.43 USD and EUR continuous compounding zero rate shoots up to 0.55%. All other market data remains the same. g) To Sam the contract is valued in USD. Using the method we discussed in class, between 10am and 10:01 amY i. What is Sam's P\&L on this trade? ii. What is the P\&L of this trade attributed to the change of EUR/USD exchange rate? iii. What is the P&L of this trade attributed to the change of EUR interest rate? iv. What is the P\&L of this trade attributed to the change of USD interest rate? v. What is the total P\&L attribution above (ie. parts ii. to iv.)? vi. What is the "unexplained P\&L" in this case? vii. Since only EUR/USD and EUR interest rate has changed in this split second crisis. Would you say your trade profit (or loss) is due to the sudden rise of EUR/USD, or the sudden rise of EUR interest rate? h) To Guillaume the contract is valued in EUR. Using the same method i. What is Guillaume's P\&L in EUR on this trade between 10am and 10:01am NY? ii. Compute Guillaume's P\&L amount in EUR between 9:59 am and 10:00am NY and Sam's P&L amount in USD in the same period. If the exchange rate at 10:00 am (ie. 1EUR= 1.30 USD) is used, are they the same? iii. Compute Guillaume's P\&L amount in EUR between 10am and 10:01am NY and Sam's P&L amount in USD in the same period. If the exchange rate at 10:00am (ie. 1EUR= 1.43 USD) is used, are they the same? iv. Do you think that Guillaume's P\&L amount in EUR is always the same as Sam's P&L amount in USD in general between two points in time? If Yes, please prove it; if No, please provide a counter example and explain why not
