Investeringstheorie (Financial Mathematics) WISB373

Investeringstheorie

Dinsdag HC 11.00 - 12.45; WerkC 13.15 - 15.00; BBL 509

Textbook

Steven Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model, Springer 2004 (ISBN 978-0-387-40100-3)

Evaluation

(i) written homework assignments contribute up to 30% to the final grade (scoring at least 80% of possible points amounts to 100% performance, i.e. contributes 3 to the final grade). A homework assignment is to be returned over the week, at the beginning of the lecture, or before the lecture in the mailbox in WG or per e-mail;

(ii) midterm test contributes up to 30% to the final grade;

(iii) final exam 40%;

(iv) herkansing

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  • 15.09 Material covered: general introduction into derivatives, the pricing problem, Section 1.1

    Homework assignments:

    1. (1 point) Consider a put option and a call option written on the same stock, with the same maturity $T=1$ (time 1) and the same strike price $K$. Using no-arbitrage arguments only, show that their prices at time $0$ must satisfy the put-call-parity relation $V_0^{put} +S_0 = V_0^{call} + K/(1+r)$.

    2. (0,5 point) Exercise 1.1

    3. (0,5 point) Exercise 1.2

    4. (0,5 point) Exercise 1.6

    5. (oefening opgave, no marking) Exercise 1.3

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  • 22.09 Material covered: Sections 1.2, 1.3, path-dependent options, discounted expected values in the RN valuation

    Homework assignments:

    1. (1 point) Exercise 1.5

    2. (1 point) Exercise 1.7

    3. (1 point) Exercise 1.8

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  • 29.09 Material covered: pp 25-38

    Homework assignments:

    1. (1 point) Exercise 2.2

    2. (1 point) Exercise 2.3

    3. (1 point) Exercise 2.4

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  • 06.10 Material covered: pp 38-49

    Homework assignments:

    1. (1,5 point) Exercise 2.8

    2. (1,5 point) Exercise 2.9

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  • 13.10 Problems on pp. 55-58

    2.5. (1 point)

    2.6 (1 point)

    2.10 (1,5 points)

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  • 20.10 Material covered: functional representation of Markov chains X_{n+1}=f_n(X_n,Y_n), application to exotic option-pricing. Pages 61-70 from the text. Preliminary discussion of the CAP model: utility, risk and lotteries.

    Homework assignments:

    3.2 (1 point)

    3.4 (1,5 points)

    3.5 (1,5 points)

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  • 27.10 Material covered: Capital asset pricing model pp 70-80.

    Problems to train for the midterm: 1.9; 2.11; 3.3

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  • 10.11 Material covered: pp 89-101.

    Homework:

    4.1 (1,5 points)

    4.2 (1 point)

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  • 17.11 Material covered: pp 101-113.

    Homework:

    4.5 (1 points)

    4.6 (2 points)

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  • 24.11 Material covered: pp 119-129.

    Homework:

    5.1 (1.5 points)

    5.4 (1.5 points)

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  • 01.12 Material covered: optimal stopping with infinite horizon, pp 129-136.

    Homework:

    5.6 (0.5 points)

    5.8 (2.5 points)

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  • 08.12 Material covered: Interest rate structures and derivatives, pp. 143-157

    Homework:

    6.3 (1 point)

    6.4 (2 points)

  • 15.12 Material covered: pp. 160-172, Brownian approximation to the binomial model and a brief introduction in the continuous time finance

    Werkcollege: Mathematics in Financial Industry (presentation by Frans Boshuizen, SNS REAAL)

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  • 12.01.10, 11:00 Werkcollege