Prerequisites are one year of Engineering and Science Mathematics or equivalent. The lab does rely on elementary concepts from Linear Algebra and Probability; students who have not taken second semester ESM (such as second year GEM students in the quantitative specialization) may pick up these concepts "on the fly" provided their general mathematical background is strong. If in doubt, please contact me directly.
Instructor: | Marcel Oliver |
Email: | m.oliver@jacobs-university.de |
Phone: | 200-3212 |
Office hours: | Mo, Tu 10:00 in Research I, 107 |
Lastname_Firstname_XX_YY.py
XX
is name of the Session number
and YY
the task number. (If a single program produces
output for several tasks, please use task number ranges.)
Session 1: | Introduction to Scientific Python; present
value, forward value; vectorized implementation and timing issues Lyuu, Section 3.1, Introduction to Scientific Python |
Session 2: |
Annuities, amortization schedule, yields, internal rate of return; root
finding methods Lyuu, Sections 3.2-3.4, Brent's method on Wikipedia |
Session 3: | Bonds, zero coupon bonds, level coupon bonds Lyuu, Section 3.5 |
Session 4: | Price volatility, Macaulay duration,
immunization (begin) Lyuu, Sections 4.1-4.2 |
Session 5: | Immunization (ctd.), convexity (brief);
The term structure of interest rates Lyuu, Sections 4.2-5.2 |
Session 6: | Forward rates, risky bonds Lyuu, Sections 5.3, 5.6 |
Session 7: | Introduction to options, payoff functions Lyuu, Chapter 7 (parts) |
Session 8: | Arbitrage-free pricing, risk-neutral probability in the one-period model, binomial tree model |
Session 9: | Calibrating the binomial tree in terms of the annualized
drift and volatility Lyuu, Section 9.3.1 |
Session 10: | Implied volatility, Put-call parity; Continuum limit of the binomial tree,
Black-Scholes formula Lyuu, Section 8.3, 9.3.2 |
Session 11: | Session 10 topics continued. |
Session 12: | Brownian motion, geometric Brownian motion Higham (2001), Section 2 |
Session 13: | Stochastic integrals, stochastic differential
equations Higham (2001), Section 3 |
Session 14: | Euler-Maruyama method Higham (2001), Sections 4 and 5 |
Session 15: | Ito formula Higham (2001), Section 8; Ito's lemma on Wikipedia |
Session 16: | Derivation of the Black-Scholes equation; banded solvers Lyuu, Sections 4.1-4.2 |
Session 17: | Implicit and explicit finite difference schemes
for the Black-Scholes equation Lyuu, Section 18.1 |
Session 18: | Implementation and testing of explicit and implicit schemes for the Black-Scholes equation; stability of time-integrators |
Session 19: | The Greeks, numerical computation of sensitivities Lyuu, Section 10.1 |
Session 20: | Implementation of sensitivity solver |
Session 21: | Parameter estimation for geometric Brownian motion Tsay, Section 6.3.4 |
Session 22: | Autocorrelation plots, QQ-plots; Elements of
time series analysis: random walk and AR(1) models Aas and Dimakos, Sections 2 and 4.2 |
Session 23: | Elements of time series analysis: very brief
introduction to MA(1) and ARMA(1,1), outlook on ARCH and GARCH models Tsay, Sections 2.5, 2.6.1 |