hw-two.pdf - Anqi Lou(al44684 Problem 2.1 M339D(unique:53970 HW 2 A fully-leveraged portfolio consists of two components the loan for the amount needed

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Anqi Lou (al44684) M339D (unique:53970) HW 2 02/12/2018 Problem 2.1 A fully-leveraged portfolio consists of two components: the loan for the amount needed to invest in the asset, and the purchased asset itself. Problem 2.2 A function ?: [0, ∞) → ℝ is said to be nonincreasing/decreasing if: For all ? > ?, ?(?) ≤ ?(?) where ?, ? ∈ [0, ∞) Problem 2.3 A function ?: [0, ∞) → ℝ is said to be nonincreasing/increasing if: For all ? > ?, ?(?) ≥ ?(?) where ?, ? ∈ [0, ∞) Problem 2.4 The payoff/profit is non-decreasing as a function of the final asset price. Problem 2.5 The payoff/profit is non-increasing as a function of the final asset price. Problem 2.6 The future value of the premiums are: 9.12 × 1.08 = 9.8496 (𝑤ℎ?? 𝑘 = 35) 6.22 × 1.08 = 6.7176 (𝑤ℎ?? 𝑘 = 40) 4.08 × 1.08 = 4.4064 (𝑤ℎ?? 𝑘 = 45) Thus, the profit function for 𝑘 = 35 is: { ?(?) − 44.8496 ?(?) ≥ 𝑘 −9.8496 ?(?) < 𝑘 The profit function for 𝑘 = 40 is: { ?(?) − 46.7176 ?(?) ≥ 𝑘 −6.7176 ?(?) < 𝑘 The profit function for 𝑘 = 45 is: { ?(?) − 49.4064 ?(?) ≥ 𝑘 −4.4064 ?(?) < 𝑘 Case 1: 𝑘 < 35 The profit for 𝑘 = 35, 40, 45 are −9.8496, −6.7176, −4.4064 The condition is not met.

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• Spring '14
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• Harshad number, Tour de Georgia, The Final, The Profit, Anqi Lou

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