(Question 1) Synthetic Option: Dynamic Hedging You investment banker work as a portfolio manager, and you want to invest in an asset(possibly foreign currency) having the following data. You want to create a put option on the investment so that at the end of the year you have losses no greater than 20 percent for the next one year. Since there is no put option (for example, there is no put option on Malaysian currency yet) on this specific asset, you plan to create a synthetic put option by engaging in a dynamic investment strategy--purchasing a portfolio composed of dynamically changing proportions of the risky asset and riskless bonds. If the interest rate is 6 percent, how much should your initial investment be in the portfolio and in the riskless bond? Assume current asset price is $100. Input Data Current Asset Price $100 Interest rate Type of Options Put(K=$90, 1yr) Put(K=$85, 1yr) Put(K=$80, 1yr) Gammal) 0.09 6% per year Option Prices Option Price Delta(4) $9.00 -0.5 $7.00 -0.4 $5.00 -0.3 0.07 0.05 (a) What is the initial position to start hedge using assets and bonds. (b) If the asset price goes down to $98(from $100 today), what is the position to make. HINTS: Delta will be changed. (Question 2) Open Interest Calculate Open Interest for the following Option Trading Day Short Trading Volume Open Interest 1 B Sells 7 Long A Buys 7 D Buys 13 E Buys 32 2 C Sells 13 A Sells 32 4 C Sells 24 5 B Sells 23 6 D Buys 24 F Buys 23 A Buys 15 C Buys 7 F Buys 14 F Sells 15 7 A Sells 7 8 B Sells 14 (Question 3) Calculate Open Interest for the following Option Trading Long Short Trading Volume Open Interest B Sells 31 31 C Sells 122 122 A Sells 12 12 Day 1 A Buys 31 2 D Buys 122 3 E Buys 12 4 D Buys 114 5 F Buys 18 6 A Buys 28 7 C Buys 17 8 F Buys 43 114 C Sells 114 B Sells 18 18 F Sells 28 28 A Sells 17 17 B Sells 43 43 (Question 4) UB corporation Exports 100 iPhone XS to Yale country at Yen 120 per machine (Yen 12,000 in total: contracted at Yen), UB's C.F.O. asks you to hedge exporting prices against foreign currency fluctuations. Current spot exchange rate is $1 = Yen 100 and the following is the price of derivatives. UB Country (U.S.A.) Yale Country (Japan) Call(Yen 120, K = $1) = $0.03 Call($1. K = Yen 120) = Yen 3 Put(Yen 120. K = $1) = $0.07 Put($1. K = Yen 120) = Yen 4 You have to consider the cost of options !!! A) If UB wants to use Call option, which Call option to buy or sell and net cash-flow at maturity? B) If UB wants to use Put option, which Put option to buy or sell and net cash-flow at maturity? *******Sample Answer******* Buy or Sell UB or Yale S to receive Exactly or At least or At most) BUY UB CALL EXACTLY pay $777 (Sample Answer) (Answers) (A)Buy or Sell UB or Yale $ to receive/pay (Exactly or At least or At most) Call Option (B)Buy or Sell UB or Yale $ to receive/pay (Exactly or At least or At most) Put Option 3 (Question 5-6) (FX Hedging) If Biden WIN: Peso UP +7%, Ruble DN -7% If Trump WIN: Peso DN -7%, Ruble UP +7% If OIL UP +8%: Peso UP +8%, Ruble UP +8%: If OIL DOWN -8%: Peso DOWN -8%, Ruble DOWN -8% What are the Total Profits of the following strategy? (Q5) Peso Ruble Oil If Bet on Presidency Currency/Oil PESO RUBLE OIL TOTAL Long Peso&Short Ruble&Long Oil Biden WIN & IF Oil UP IF Oil Down PESO RUBLE OIL TOTAL Short Peso&Long Ruble&Long Oil Trump WIN & IF Oil UP IF Oil Down (06) Peso Ruble Oil If Bet on Presidency Currency/Oil PESO RUBLE OIL TOTAL Long Peso&Short Ruble&Short Oil Biden WIN & IF Oil UP IF Oil Down PESO RUBLE OIL TOTAL Short Peso&Long Ruble&Short Oil Trump WIN & IF Oil UP IF Oil Down 27 - Q8) Stock = $77, C(K=$80) = $5, P(K=$80) = $6 Question 7)(Normal, Delete, Wild) What are the Max Loss and Maxi Profits per share in (Buy Stock and Buy Put option) Name Strategy Nick Name Total Profit or Losses (Including Stock and Option) Maximum Profit Maximum Loss $ $ Hannah Buy S & Buy Put Married Put When S = $ When S, = $ (Question 8)(Normal, Delete, Wild) What are the Max Loss and Max Profits per share in (Buy stock and Sell Call option) Name Strategy Nick Name Total Profit or Losses (Including Stock and Option) Maximum Profit Maximum Loss Melly Buy S & Sell Call Covered Call $ $ When S,= $ When S, $ (Question 1) Synthetic Option: Dynamic Hedging You investment banker work as a portfolio manager, and you want to invest in an asset(possibly foreign currency) having the following data. You want to create a put option on the investment so that at the end of the year you have losses no greater than 20 percent for the next one year. Since there is no put option (for example, there is no put option on Malaysian currency yet) on this specific asset, you plan to create a synthetic put option by engaging in a dynamic investment strategy--purchasing a portfolio composed of dynamically changing proportions of the risky asset and riskless bonds. If the interest rate is 6 percent, how much should your initial investment be in the portfolio and in the riskless bond? Assume current asset price is $100. Input Data Current Asset Price $100 Interest rate Type of Options Put(K=$90, 1yr) Put(K=$85, 1yr) Put(K=$80, 1yr) Gammal) 0.09 6% per year Option Prices Option Price Delta(4) $9.00 -0.5 $7.00 -0.4 $5.00 -0.3 0.07 0.05 (a) What is the initial position to start hedge using assets and bonds. (b) If the asset price goes down to $98(from $100 today), what is the position to make. HINTS: Delta will be changed. (Question 2) Open Interest Calculate Open Interest for the following Option Trading Day Short Trading Volume Open Interest 1 B Sells 7 Long A Buys 7 D Buys 13 E Buys 32 2 C Sells 13 A Sells 32 4 C Sells 24 5 B Sells 23 6 D Buys 24 F Buys 23 A Buys 15 C Buys 7 F Buys 14 F Sells 15 7 A Sells 7 8 B Sells 14 (Question 3) Calculate Open Interest for the following Option Trading Long Short Trading Volume Open Interest B Sells 31 31 C Sells 122 122 A Sells 12 12 Day 1 A Buys 31 2 D Buys 122 3 E Buys 12 4 D Buys 114 5 F Buys 18 6 A Buys 28 7 C Buys 17 8 F Buys 43 114 C Sells 114 B Sells 18 18 F Sells 28 28 A Sells 17 17 B Sells 43 43 (Question 4) UB corporation Exports 100 iPhone XS to Yale country at Yen 120 per machine (Yen 12,000 in total: contracted at Yen), UB's C.F.O. asks you to hedge exporting prices against foreign currency fluctuations. Current spot exchange rate is $1 = Yen 100 and the following is the price of derivatives. UB Country (U.S.A.) Yale Country (Japan) Call(Yen 120, K = $1) = $0.03 Call($1. K = Yen 120) = Yen 3 Put(Yen 120. K = $1) = $0.07 Put($1. K = Yen 120) = Yen 4 You have to consider the cost of options !!! A) If UB wants to use Call option, which Call option to buy or sell and net cash-flow at maturity? B) If UB wants to use Put option, which Put option to buy or sell and net cash-flow at maturity? *******Sample Answer******* Buy or Sell UB or Yale S to receive Exactly or At least or At most) BUY UB CALL EXACTLY pay $777 (Sample Answer) (Answers) (A)Buy or Sell UB or Yale $ to receive/pay (Exactly or At least or At most) Call Option (B)Buy or Sell UB or Yale $ to receive/pay (Exactly or At least or At most) Put Option 3 (Question 5-6) (FX Hedging) If Biden WIN: Peso UP +7%, Ruble DN -7% If Trump WIN: Peso DN -7%, Ruble UP +7% If OIL UP +8%: Peso UP +8%, Ruble UP +8%: If OIL DOWN -8%: Peso DOWN -8%, Ruble DOWN -8% What are the Total Profits of the following strategy? (Q5) Peso Ruble Oil If Bet on Presidency Currency/Oil PESO RUBLE OIL TOTAL Long Peso&Short Ruble&Long Oil Biden WIN & IF Oil UP IF Oil Down PESO RUBLE OIL TOTAL Short Peso&Long Ruble&Long Oil Trump WIN & IF Oil UP IF Oil Down (06) Peso Ruble Oil If Bet on Presidency Currency/Oil PESO RUBLE OIL TOTAL Long Peso&Short Ruble&Short Oil Biden WIN & IF Oil UP IF Oil Down PESO RUBLE OIL TOTAL Short Peso&Long Ruble&Short Oil Trump WIN & IF Oil UP IF Oil Down 27 - Q8) Stock = $77, C(K=$80) = $5, P(K=$80) = $6 Question 7)(Normal, Delete, Wild) What are the Max Loss and Maxi Profits per share in (Buy Stock and Buy Put option) Name Strategy Nick Name Total Profit or Losses (Including Stock and Option) Maximum Profit Maximum Loss $ $ Hannah Buy S & Buy Put Married Put When S = $ When S, = $ (Question 8)(Normal, Delete, Wild) What are the Max Loss and Max Profits per share in (Buy stock and Sell Call option) Name Strategy Nick Name Total Profit or Losses (Including Stock and Option) Maximum Profit Maximum Loss Melly Buy S & Sell Call Covered Call $ $ When S,= $ When S, $