Buffa_FNCE4040_Sample_MidtermExam1

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Derivative Securities, Fall 2023 FNCE4040, Sample Midterm Exam 1 FNCE 4040 Derivative Securities Sample Midterm Exam 1 Name: ID#: Section#: Instructions: • You have 80 minutes to answer the questions. • The exam is closed-book: you are not allowed to consult any books, notes, readings, material distributed in class, or other resources. You are allowed to consult the formula sheet that has been distributed for this exam. • For your calculations, you are allowed to use a blank Excel spreadsheet (no pre-programmed macros or pre-populated cells), or a scientific calculator. • The exam is an individual effort. Students must not compare questions, answers, or solution methods with anyone during the exam. • The honor code applies. © Buffa-Garc´ ıa, Leeds School of Business Page 1 of 4

Derivative Securities, Fall 2023 FNCE4040, Sample Midterm Exam 1 Short Questions – 30 points 1. The seller of a put option has the right to not exercise the option at the expiration date. (a) True (b) False 2. An American option can be exercised at the expiration date, as well as at any point in time before it. (a) True (b) False 3. If an option is out-of-the money, its time value can be negative. (a) True (b) False 4. The payoff of a butterfly spread is equal to: (a) max( S T − K 1 , 0) − max( S T − K 2 , 0) + 2 × max( S T − ( K 1 + K 2 ) , 0) (b) max( S T − K 1 , 0) + max( S T − K 2 , 0) − 2 × max( S T − ( K 1 + K 2 ) / 2 , 0) (c) max( S T − K 1 , 0) − max( S T − K 2 , 0) + max(( K 1 + K 2 ) / 2 − S T , 0) (d) max( S T − K 1 , 0) + max( S T − K 2 , 0) − max(2 × S T − ( K 1 + K 2 ) / 2 , 0) 5. Consider buying a put option with a strike of $ 50, which costs $ 7. What would be your profits if the underlying asset trades for $ 57 at the expiration date? What would be your profits if the underlying asset trades for $ 41 at the expiration date? 6. A call option on MSFT with a strike of $ 40 and a one year maturity is trading for $ 7.19. MSFT is trading for $ 40, and the annual risk-free rate is 1%. What should be the price of a put option with the same strike and maturity, in the absence of arbitrage? © Buffa-Garc´ ıa, Leeds School of Business Page 2 of 4

Derivative Securities, Fall 2023 FNCE4040, Sample Midterm Exam 1 Term Structure of Interest Rates – 35 points 1. The following three bonds are available for trading: Maturity Coupon Rate Face Value Price ( years ) ( annual ) ( $ ) ( $ ) Bond A 3 10% 1000 986.89 Bond B 3 20% 1000 1242.59 Bond C 2 30% 1000 1421.18 Assume all bonds pay coupons annually. (a) What is the term structure in this economy? Determine r 1 , r 2 , and r 3 . (b) What are the forward rates in this economy? In particular, spell out what rate you can get for an investment at date 1 that matures at date 2, and for an investment at date 2 that matures at date 3. (c) Suppose that we have a fourth bond, bond D, that pays annual coupons of 5%, face value of $ 1000, and a maturity of 3 years. What is the no-arbitrage value of bond D? (d) How would you replicate the future cash flows of bond D by trading bonds A, B, and C given above? Give an explicit description of the units of each bond in the replicating portfolio. (e) You discover that bond D is currently traded for $ 855- $ 860 (bid-ask prices). Can you create an arbitrage strategy that involves trading bond D, as well as the other three bonds given above? Give an explicit description of the units of each bond in your arbitrage strategy, as well as the arbitrage profit. © Buffa-Garc´ ıa, Leeds School of Business Page 3 of 4

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Derivative Securities, Fall 2023 FNCE4040, Sample Midterm Exam 1 Option Trading – 35 points 1. Consider the following options on the same underlying asset with expiration in two months: • Call option with strike price $ 80 is currently priced at $ 14.6; • Put option with strike price $ 80 is currently priced at $ 7.2; • Put option with strike price $ 95 is currently priced at $ 13.8. The annual risk-free rate is 3% and the term structure is flat (consider annual compounding). The underlying asset is not expected to pay any dividends in the next two months. (a) Based on the options above, what should be the no-arbitrage price of the underlying asset? (b) Note that at the moment there are no call options with strike price $ 95 (on the same underlying asset and with expiration in two months) that are traded in the market. Based on the options above, what should be the no-arbitrage price of that call option with strike price $ 95? (c) You realize that someone has just written some call options with strike price $ 95, which are now traded for $ 7.4. Is there an arbitrage strategy that you can implement without trading the underlying asset? Give an explicit description of the units of each asset in your arbitrage strategy, as well as the arbitrage profit. (d) (***, 10 extra points ) If the current market price of the underlying asset is actually 5% higher than the no-arbitrage price you obtained in part (a), is there a more profitable arbitrage strategy than the one you identified in part (c)? Give an explicit description of the most profitable arbitrage strategy that you can create by trading the options above, bonds, and the underlying asset. © Buffa-Garc´ ıa, Leeds School of Business Page 4 of 4