Fall Semester 2011

Derivatives Lab

Syllabus

Summary:

This lab is an introduction to Mathematical Finance, in particular derivatives pricing, via computer experiments. It is designed for second year ACM students, but should also appeal to a wider audience.

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.

Contact Information:

Instructor:	Marcel Oliver
Email:	m.oliver@jacobs-university.de
Phone:	200-3212
Office hours:	Tu, We 10:00 in Research I, 107

Time and Place:

Mo, Tu 15:45-18:30 in the CS Lecture Hall (Research I)

Literature:

Yuh-Dauh Lyuu, "Financial Engineering & Computation: Principles, Mathematics, Algorithms," Cambridge University Press, 2002.
Some chapters of this book are available from the author's web page.
Sheldon M. Ross, "An Introduction to Mathematical Finance: Options and Other Topics," Cambridge University Press, 1999.
Desmond J. Higham, An algorithmic introduction to numerical simulation of stochastic differentialequations, SIAM Review 43 (2001), 525-546.
Desmond J. Higham, Black-scholes for scientific computing students, Computing in Science and Engineering 6 (2004), 72-79.

Session Overview

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)

Last modified: 2012/05/07
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2011/acm221/index.html
Marcel Oliver (m.oliver@jacobs-university.de)