Topics include binomial tree models, discrete Brownian paths, stochastic ODEs, Monte-Carlo methods, finite differences solutions for the Black-Scholes equation, and an introduction to time series analysis, parameter estimation, and calibration. Students will program and explore all basic techniques in a numerical programming environment and apply these algorithms to real data whenever possible.
Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | We/Th 10:00 in Research I, 107 |
TA: | Kim Philipp Jablonski |
Email: | k.jablonski@jacobs-university.de |
git
; detailed
instructions will be posted on this page.
01/09/2016: | Introduction to Scientific Python |
06/09/2016: | Basic notions from finance (present
value, forward value, annuities, amortization schedule, yields,
internal rate of return); Basic computational tools (vectorized
formulation of problems, timing issues, root finding methods). Lyuu, Sections 3.1-3.4 |
08/09/2016: | Introduction to git |
13/09/2016: | Bonds, zero coupon bonds, level coupon bonds Lyuu, Section 3.5 |
15/09/2016: | Immunization, Macaulay duration,
immunization (begin) Lyuu, Sections 4.1-4.2 |
20/09/2016: | Immunization (ctd.), convexity (brief);
The term structure of interest rates Lyuu, Sections 4.2-5.2 |
22/09/2016: | No class |
27/09/2016: | Options: introduction, single-period model, risk-neutral probabilites, binomial tree mathod (start) |
29/09/2016: | Binomial tree method (implementation) |
04/10/2016: | Binomial tree method: scaling and calibration |
06/10/2016: | Binomial tree method: visualization, convergenc; call-put parity |
11/10/2016: | Central limit theorem for binomial distributions; derivation of the Black-Scholes formula |
13/10/2016: | Brownian motion |
18/10/2016: | Stochastic integrals |
20/10/2016: | Stochastic differential equations, Euler-Maruyama method |
27/10/2016: | Weak and strong convergence |
01/11/2016: | Ito Lemma |
03/11/2016: | Derivation of the Black-Scholes equation; finite differences |
10/11/2016: | Stability; explicit vs. implicit timestepping, tridiagonal systems |
15/11/2016: | |
17/11/2016: | |
22/11/2016: | |
24/11/2016: | |
29/11/2016: | |
01/12/2016: | |
06/12/2016: |