# Monte Carlo and Quantization Methods in Quantitative Finance

04.05.2017 – 06.05.2017

### Abstract

### Schedule

- Thursday, May, 4th, 2017. 09:00 - 17:30
- Friday, May, 5th, 2017. 09:00 - 17:30
- Third day TBD

### Venue

The workshop takes place at

**quantLab** - Room B 121

LMU Institute of Mathematics

Theresienstr. 39

80333 Munich

A detailed location plan can be found here.

### Contact

### Tentative Schedule

Morning Session 1 |
9:00 - 10:30 |

Morning Session 2 |
11:00 - 12:30 |

Afternoon Session 1 |
14:00 - 15:30 |

Afternoon Session 2 |
16:00 - 17:30 |

**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 **

**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**

**Thomas McWalter**

Thomas is an Adjunct Associate Professor in the area of Mathematical finance at both the University of Cape Town and the University of Johannesburg. He teaches and supervises masters and doctoral students specialising in numerical methods in finance. His research interests include simulation and parameter estimation in stochastic processes, with applications to both finance and biology.

** Ralph Rudd**

After completing his undergraduate degree in Theoretical Physics and Applied Mathematics, Ralph Rudd spent two years creating and running digital fluid simulations for the visual effects industry. He returned to academia to obtain his Masters degree in Mathematical Finance and is currently busy with his doctoral studies at the University of Cape Town. He is supervised by Professor Thomas McWalter from UCT, Professor Jörg Kienitz from Bergische Universität Wuppertal and Professor Eckhard Platen from the University of Technology, Sydney.

### Prof. Dr. Christian Fries

Christian Fries is head of model development at DZ Bank’s risk control and Professor for Applied Mathematical Finance at Department of Mathematics, LMU Munich.

His current research interests are hybrid interest rate models, Monte Carlo methods, and valuation under funding and counterparty risk. His papers and lecture notes may be downloaded from http://www.christian-fries.de/finmath

He is the author of “Mathematical Finance: Theory, Modeling, Implementation”, Wiley, 2007 and runs www.finmath.net.

The payment of a workshop fee is required, according to the following table:

Rate |
Type of Participant |

950 € | Practitioners |

350 € | Academics |

### Registration and Contact

The workshop will take place in a computer equipped room with limited places. To register send an email to: email@christian-fries.de