Workgroup Financial Mathematics

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Monte Carlo and Quantization Methods in Quantitative Finance

Lead by Prof. Dr. Thomas McWalter, Prof. Dr. Jörg Kienitz, Ralph Rudd and Prof. Dr. Christian Fries

Schedule and Venue

May 4th, 2017

Morning Session 1
8:30 - 10:00
Morning Session 2
10:30 - 12:00
Afternoon Session 1
14:00 - 15:30
Afternoon Session 2
16:00 - 17:30

Room B 121

May 5th, 2017

Exercise session and/or final Exam
9:00 - 12:00

Registration and Contact: To register email to:

Course Description

to be announced

Tentative Agenda

Day1: Monte Carlo Methods (4 x 90 min lectures)

Lecture 1: Ralph Rudd

  • Overview
  • Pseudo-random numbers
  • Generating random numbers from other distributions
  • Normal and multi-variate normal
  • MC integration and convergence

Lecture 2: Thomas McWalter

  • Overview
  • Brownian motion, Ito and Geometric Brownian motion
  • Path SDEs: Euler, Milstein, simplified weak second order: construction and weak and strong order
  • Risk neutral pricing of derivatives

 Lecture 3: Ralph Rudd

  • Overview
  • Option pricing
  • Variane reduction: antithetic variates, control variates, importance sampling, stratification
  • Advanced pricing (part 1): American options using least-squares MC

Lecture 4: (Thomas McWalter)

  • Advanced Pricing (part 2): Other path dependent options (barriers, look-backs, etc)
  • Quasi-Monte Carlo
  • Introduction to Low Discrepancy Sequences
  • Convergence: Discrepancy, Star Discrepancy and K-H Inequality
  • Halton and Hammersley Sequences
  • Sobol Sequences
  • Examples

Day 2: Quantization Methods (4 x 90 min lectures)

Lecture 1: Vector Quantization (Ralph Rudd)

  • Overview and formulation of the problem
  • Numerical Methods: NLloyd’s Algorithm (fixed point), Competitive Learning Vector Quantization
  • Newton-Raphson
  • Efficient Implementation
  • Convergence
  • Examples

Lecture 2: Recursive Marginal Quantization (Thomas McWalter)

  • Overview and formulation of the problem
  • Algorithm
  • Convergence
  • Higher-order Extensions and Convergence
  • Adapting RMQ to correctly account for Boundary Behaviour
  • Pricing Examples

Lecture 3: Advanced Pricing and Stochastic Volatility (Ralph Rudd)

  • Overview
  • American Options using Backward Dynamic Programming
  • Barrier Options using the Transition Kernel Approach
  • Two Factor Models using Joint RMQ
  • Algorithm
  • Exact and Approximate Joint Probabilities
  • Efficient Implementation
  • Pricing Under Stochastic Volatility Models (Heston, Stein and Stein, SABR)

Lecture 4: Advanced Quantization Applications (Thomas McWalter)

  • Using RMQ for Calibration
  • Functional Quantization
  • Cross Products of Quantizers
  • Stratification of Principle components
  • Optimal allocation

Day 3: TBD


to be announced.

For whom is this course?

Target Participants: Master students of Mathematics or Business Mathematics.

Pre-requisites: Probability Theory, Finanzmathematik II (Stochastic Calculus).

Applicable credits:  Students will receive 3 ECTS Points upon successful participation that may be attributed to any one of the following modules: WP18/1 for students enrolled in the LMU Master Mathematics programme. WP20, WP22 or WP23 for students enrolled in the LMU Master Business Mathematics (Wirtschaftsmathematik) programme.


The course will also include exercise sessions in which you will work hands-on with implementations of the presented techniques and models. Active participation in the exercise sessions is strongly recommended.


The written exam is open-book, that is, all notes, books, solutions of exercises etc. may be used. Personal electronic devices of any kind are not allowed. To participate, please bring to the exam your ID card or passport and your student card. Please be on time.