HW 1

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Baruch College, CUNY *

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9797

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Finance

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Jan 9, 2024

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docx

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7

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Review Test Submission: HW1-Forward Pricing User William L Lopez Flores Course 2023 Fall Term (1) Options Markets FIN 9797 UWA[16297] (Baruch College) Test HW1-Forward Pricing Started 9/12/23 6:17 PM Submitted 9/12/23 8:52 PM Due Date 9/13/23 1:00 PM Status Completed Attempt Score 130 out of 130 points Time Elapsed 2 hours, 34 minutes Results Displayed All Answers, Submitted Answers, Correct Answers Question 1 10 out of 10 points "Suppose you are long 3 shares of a stock (without dividend payment), what will be your payoff at time T. Describe the payoff using the following equation: Payoff = A + B*Stock price (S_T). What is the intercept, A? [a]. What is the slope? [b] (Answer in integers)" Specified Answer for:a & 0 Specified Answer for:b & 3 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 0 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 3 Question 2 10 out of 10 points "Suppose you are long one share of a stock and assume that the stock pays $5 dividend at T (and nothing in between). Write your payoff as A+ B*S_T, What is the intercept, A? [a]. What is the slope? [b] If the stock price at T (S_T) is $100, what is your payoff at T? [c] (All answer in integers)" Specified Answer for:a @ 5 Specified Answer for:b @ 1 Specified Answer for: ¢ @ 105 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 5 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 1 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match 105
Question 3 10 out of 10 points "Suppose you are long 10 shares of a stock and assume that the stock pays $5 dividend per share at T (and nothing in between). If the stock price at T (S_T) is $100, how much is the payoff at T? [a] Write the payoff function as A+ B*S_T, what is A? [b] What is B? [c]" Specified Answer for:a & 1050 Specified Answer for:b & 50 Specified Answer for:c @ 10 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity @ Exact Match 1050 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 50 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match 10 Question 4 10 out of 10 points Suppose the current price of a stock is $100. The stock pays $5 dividend per share once per year. The continuously compounded interest rate of 5%. What is the fair forward price on the stock with a maturity of 2 years? (round to 2 decimals) Selected Answer: & 100.26 Correct Answer: @& 100.26 Answer range +/- 0.02 (100.24 - 100.28 ) Question 5 10 out of 10 points "What is the payoff function of a zero-coupon bond with maturity date T and par value of $1? Write the payoff in terms of A+ B*S_T (for some stock price S_T). What is A? (integer) [a]What is B? (integer) [b] If the continuously compounding interest rate is 5%, how much is this bond worth today when T=2? (round to 3 decimals) [c] " Specified Answer for:a @ 1 Specified Answer for:b @ 0 Specified Answer for: ¢ @ 0.905 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 1 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 0 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match 0.905 Question 6 10 out of 10 points "Suppose you borrow 100 dollars to buy one share of a stock today (the stock price SO is $100), the interest rate is 5% per year (continuous compounding). The stock does not pay dividend. If two years later (T=2), the stock price (S_T) is $120, what is your payoff at time T? (round to 2 decimals) " Selected Answer: & 9.48 Correct Answer: & 9.48 Answer range +/- 0.02 (9.46 - 9.50 )
Question 7 10 out of 10 points "Suppose you borrow 100 dollars to buy one share of a stock today (the stock price (S0) is $100), the interest rate is 5% (continuous compounding). The stock does not pay dividend. If there are forward contracts traded on this stock with expiry T=2, what should be the fair forward price with 2-year maturity? (round to 2 decimals) [a] Design a trading strategy to make money if the forward price is $105. The strategy is: You enter into a ""long [c] the stock at $105 at time T. You also enter a ""long' decimals) [e]. " Specified Answer for:a @ 110.52 Specified Answer for: b @& long Specified Answer for: ¢ @& buy Specified Answer for:d @& short Specified Answer for:e @& 5.52 Correct Answers for: a Evaluation Method & Exact Match Correct Answers for: b Evaluation Method @ Exact Match Correct Answers for: c Evaluation Method & Exact Match Correct Answers for: d Evaluation Method & Exact Match Correct Answers for: e Evaluation Method & Exact Match Question 8 i Correct Answer 110.52 Correct Answer long Correct Answer buy Correct Answer short Correct Answer 5.52 Case Sensitivity Case Sensitivity Case Sensitivity Case Sensitivity Case Sensitivity or ""short™ [b] position in the forward contract at the quoted price of $105 to ""buy™ or ""sell" or ""short™ [d] position on the stock today. You will make a profit of (round to 2 10 out of 10 points "The current stock price (S_0) is $100, and interest rate is 5% (continuous compounding). The stock does not pay dividend. What is the fair forward price with T=2? (round to 2 decimals)? [a] Suppose you are long 1 contract (100 shares) of a forward on the stock with expiry T=2 and with a delivery price (K) of $100. What is its current value of your long forward position? (round to integer)[b] What the value will be if the contract delivery price is $120 instead? (round to integer)[c]" Specified Answer for:a @ 110.52 Specified Answer for:b @ 952 Specified Answer for: ¢ & -858 Correct Answers for: a Evaluation Method & Exact Match Correct Answers for: b Evaluation Method & Exact Match Correct Answers for: c Evaluation Method & Exact Match Correct Answer 110.52 Correct Answer 952 Correct Answer -858 Case Sensitivity Case Sensitivity Case Sensitivity
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Question 9 10 out of 10 points "The current stock price (S_0) is $100, and interest rate is 5% (continuous compounding). The stock pays $2 dividend once per year. What is the fair forward price with T=2? (round to 2 decimals)? [a] Suppose you are long 1 contract (100 shares) of a forward on the stock with expiry T=2 and with a delivery price (K) of $100. What is its current value of your long forward position? (round to integer)[b] What the value will be if the contract delivery price is $120 instead? (round to integer)[c]" Specified Answer for:a @ 106.41 Specified Answer for: b @ 580 Specified Answer for:c @ -1229 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 106.41 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 580 Correct Answers for: c Evaluation Method Correct Answer Case Sensitivity & Exact Match -1229 Question 10 10 out of 10 points "Suppose a stock index has a current level (S0) at $100. The interest rate is 5% (continuous compounding). The stock index has a dividend yield of 2% per year (continuous compounding). What is the fair 2-year forward price on the index? (round to 2 decimals) [a] Suppose you have a portfolio that has 3 long forward contracts on the index with T=2 and a delivery price (K) of $100, what is the current value of your portfolio? (round to integer) [b] What is the current value if the delivery price is $120? [c]" Specified Answer for:a @ 106.18 Specified Answer for:b & 1679 Specified Answer for: ¢ & -3750 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 106.18 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity @ Exact Match 1679 Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match -3750 Question 11 10 out of 10 points Current stock price (S0) is $100. The stock pays $2 dividend per quarter. The interest rate is 5% per year (continuous compounding). What is the fair forward price on the stock with a maturity of 2 years? (There will be 8 dividend payments. Round answer to 2 decimals) Selected Answer: & 93.79 Correct Answer: & 93.79 Answer range +/- 0.02 (93.77 - 93.81)
Question 12 10 out of 10 points "MSFT currently trades at $105. It pays $0.5 dividend at the end of each quarter. Assume this is the beginning of a quarter so that the next payment will be exactly three months (1/4 year) from now. (a) Compute the forward price for MSFT at (i) 0.5-year maturity (round to 2 decimals) [a], (ii) 1-year maturity (round to 2 decimals) [b]. (b) Compute the present value (round to integers) of 2 long 1-year forward contracts (100 shares per contract) on MSFT with a delivery price of (i) $80 [c], (ii) $100 [d], (iii) $120 [e]. (c) Compute the terminal payoff (round to integers) of 3 long 1-year forward contracts on MSFT with a delivery price of $105 if the stock price one year later (at expiry) is (i) $70 [f], (i) $100 [g], (i) $130 [h]. Note: Assume a continuously compounding dollar interest rate of 5% for all maturities, whenever applicable." Specified Answer for:a @ 106.65 Specified Answer for: b @ 108.35 Specified Answer for: c @ 5393 Specified Answer for:d @ 1588 Specified Answer for:e @ -2217 Specified Answer for: f @ -10500 Specified Answer for: g @ -1500 Specified Answer for: h & 7500 Correct Answers for: a Evaluation Method Correct Answer & Exact Match 106.65 Case Sensitivity Correct Answers for: b Evaluation Method Correct Answer & Exact Match 108.35 Case Sensitivity Correct Answers for: ¢ Evaluation Method & Exact Match Correct Answers for: d Evaluation Method & Exact Match Correct Answers for: e Evaluation Method & Exact Match Correct Answers for: f Evaluation Method & Exact Match Correct Answers for: g Evaluation Method & Exact Match Correct Answers for: h Evaluation Method & Exact Match Correct Answer 5393 Correct Answer 1588 Correct Answer -2217 Correct Answer -10500 Correct Answer -1500 Correct Answer 7500 Case Sensitivity Case Sensitivity Case Sensitivity Case Sensitivity Case Sensitivity Case Sensitivity
Question 13 10 out of 10 points "Currently British pound (GBPUSD) trades at $1.29. The pound continuously compounding interest rates are at 1.00%, 1.20%, and 1.35% at 1-year, 3-year, and 5-year maturities, respectively. (a) Compute the forward price of pound (round to 2 decimals) at (i) 1-year maturity [a], (ii) 3-year maturity [b], (iii) 5-year maturity [c]. (b) If your portfolio contains long 2000 contracts on pound 1-year forward with a delivery price of $1.30, and short 2000 contracts on pound 5-year forward with the delivery price of $1.50, whatOs the current value (round to integers) of (i) your long position in the 1-year forward [d], (ii) your short position in the 5- year forward [e], and (iii) your total portfolio [f]. (c) Suppose you decide to hold your above portfolio for one year. One-year later, the pound price goes up to $1.40. The dollar interest rate curve remains flat at 5%, and the pound interest rate curve also becomes flat at 1%. What will be the value (round to integers) of (i) your long position [g], (ii) your short position [h], and (iii) your total portfolio then. [i] Note: Assume a continuously compounding dollar interest rate of 5% for all maturities, whenever applicable. Keep two decimals" Specified Answer for:a @ 1.34 Specified Answer for: b @& 1.45 Specified Answer for: ¢ @& 1.55 Specified Answer for:d @ 8113 Specified Answer for:e @ -7520 Specified Answer for: f @& 594 Specified Answer for: g @ 20000 Specified Answer for: h @ -23402 Specified Answer for:i @ -3402 Correct Answers for: a Evaluation Method Correct Answer Case Sensitivity & Exact Match 1.34 Correct Answers for: b Evaluation Method Correct Answer Case Sensitivity & Exact Match 1.45
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Correct Answers for: ¢ Evaluation Method Correct Answer Case Sensitivity & Exact Match 1.55 Correct Answers for: d Evaluation Method Correct Answer Case Sensitivity & Exact Match 8113 Correct Answers for: e Evaluation Method Correct Answer Case Sensitivity & Exact Match -7520 Correct Answers for: f Evaluation Method Correct Answer Case Sensitivity & Exact Match 594 Correct Answers for: g Evaluation Method Correct Answer Case Sensitivity @ Exact Match 20000 Correct Answers for: h Evaluation Method Correct Answer Case Sensitivity & Exact Match -23402 Correct Answers for: i Evaluation Method Correct Answer Case Sensitivity Exact Match -3402 @