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: | Tu, We 10:00 in Research I, 107 |
Session 1: | Introduction to Numerical Python; present value, forward value; implementation and timing issues |
Session 2: | Annuities, amortization schedule, internal rate or return; root finding methods |
Session 3: | Bonds, yields, level coupon bonds |
Session 4: | Macaulay duration, convexity |
Session 5: | The term structure of interest rates |
Session 6: | Immunization |
Session 7: | Review and discussion of finance topics |
Session 8: | Introduction to options, payoff functions, arbitrage-free pricing |
Session 9: | Option pricing via the binomial tree model (European calls) |
Session 10: | Continuum limit of the binomial tree, Black-Scholes formula |
Session 11: | Put options, implied volatility |
Session 12: | Brownian motion, geometric Brownian motion |
Session 13: | Brownian motion (continued) |
Session 14: | Stochastic integrals, stochastic differential equations, Euler-Maruyama method |
Session 15: | Ito formula |
Session 16: | Ito formula (continued) |
Session 17: | Black-Scholes equation, banded solvers |
Session 18: | Black-Scholes equation (continued), numerical methods |
Session 19: | Implementation of explicit and implicit solver for the Black-Scholes equation |
Session 20: | The Greeks, numerical computation of sensitivities |
Session 21: | Implementation of sensitivity solver |
Session 22: | Elements of time series analysis; volatility vs. drift estimation, autocorrelation plots, QQ-plots |
Session 23: | Elements of time series analysis (continued) |