Exercises Chapter 1

Question 1

Sheet 1, Ex 1

Answer 1

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Question 2

Sheet 1, Ex 2

Answer 2

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Question 3

Sheet 1, Ex 3

Answer 3

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Question 4

Sheet 1, Ex 4

Answer 4

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Question 5

Sheet 2, Ex “Cross-hedging”

Answer 5

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Question 6

Sheet 2, Ex “Swaps”

Answer 6

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Question 7

Sheet 2, Ex “Speed of a Bond”

Answer 7

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Question 8

Sheet 3, Ex 1 “Call option properties”

Mistake in 1.3, see https://forum.math.ethz.ch/t/assignment-3-questions/1420/7

Answer 8

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Question 9

Sheet 3, Ex 2 “prove proposition 1.4.19”

UPDATE

Answer 9

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Question 10

Sheet 4, Ex 1 “call-call and call-put options.

Answer 10

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Question 11

A Bull Spread consist in buying a call with strike K 1 and selling a call with strike K 2 > K 1 .

1) Does this strategy have an initial cost?
2) Calculate and draw the corresponding payoff.
3) What do you think could be the purpose of this strategy?

Answer 11

Sheet 4, Ex 2 “Bull spread”

Question 12

A Bottom Straddle consists in buying a call and a put with the same strike and the same maturity. Same questions
as in the previous exercise.

Answer 12

Sheet 4, Ex 3 “bottom straddle”

Question 13

A Butterfly Spread consists in selling 2 calls with strike K 2 and buying a Call with strike K 1 and a call with
strike K 3 , with 0 ≤ K 2 − K 1 = K 3 − K 2 . Same questions as in the previous exercise.

Answer 13

Sheet 4, Ex 4 “butterfly spread”

Question 14

Sheet 4, Ex 5 “Barrier option”

Answer 14

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Question 15

Sheet 5, Ex 1 “On American Calls with dividends”

Answer 15

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Question 16

Sheet 5, Ex 2 “Asymptotics for the CRR model”

Answer 16

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