= For the purpose of this question, we ignore all bid/offer spreads, working only with mid prices. Let the EURUSD exchange rate be 1.4200. Consider a 6-month option to buy USD 1,525,000 and sell EUR 1,000,000, in a spot transaction. Assume that the volatility is constant at 15%, and that rusd = 2%, PEUR 1%. Q1: Compute the present value (premium) of the option in both USD and in EUR. Which currency will be the premium currency, according to standard market practice? Q2: Compute all four possible market quotes for the option premium (see Lecture 2). Q3: Compute all four possible foreign currency deltas (spot and forward, with and without premium adjustment). Which one is the market standard? Q4: Now consider a digital option paying USD 1,000,000 if the EURUSD exchange rate is larger than 1.4500, 6 months from now. What is today's value of this option (expressed both in USD and EUR)? Q5: Same option as in Q4, but the payment is EUR 1,000,000 (rather than USD 1,000,000). What is today's value? Q6: Go back to the ordinary European option in questions Q1-Q3, but now make the payout a forward contract, rather than a spot contract. Specifi- cally, at the 6-month expiration date of the option, the option holder has the right to enter into a 3-month forward contract where USD 1,525,000 is bought and EUR 1,000,000 is sold. (So, to clarify: if the option is exercised 6 month from today, the final exchange of currency amounts takes place 9 months from today). What is the present value of this contract, in USD and in EUR? = For the purpose of this question, we ignore all bid/offer spreads, working only with mid prices. Let the EURUSD exchange rate be 1.4200. Consider a 6-month option to buy USD 1,525,000 and sell EUR 1,000,000, in a spot transaction. Assume that the volatility is constant at 15%, and that rusd = 2%, PEUR 1%. Q1: Compute the present value (premium) of the option in both USD and in EUR. Which currency will be the premium currency, according to standard market practice? Q2: Compute all four possible market quotes for the option premium (see Lecture 2). Q3: Compute all four possible foreign currency deltas (spot and forward, with and without premium adjustment). Which one is the market standard? Q4: Now consider a digital option paying USD 1,000,000 if the EURUSD exchange rate is larger than 1.4500, 6 months from now. What is today's value of this option (expressed both in USD and EUR)? Q5: Same option as in Q4, but the payment is EUR 1,000,000 (rather than USD 1,000,000). What is today's value? Q6: Go back to the ordinary European option in questions Q1-Q3, but now make the payout a forward contract, rather than a spot contract. Specifi- cally, at the 6-month expiration date of the option, the option holder has the right to enter into a 3-month forward contract where USD 1,525,000 is bought and EUR 1,000,000 is sold. (So, to clarify: if the option is exercised 6 month from today, the final exchange of currency amounts takes place 9 months from today). What is the present value of this contract, in USD and in EUR
