Pacific Institute for the Mathematical Sciences - PIMS

Monte Carlo methods make use of randomness to compute solutions to large-scale problems in a fraction of the time of alternative approaches. First called `Monte Carlo' methods by physicists working on the Manhattan Project in the 1940s, they are used now in diverse fields such as computer graphics,reliability engineering, environmental modeling, nuclear physics, molecular chemistry, and many others.

The focus of this course will be on financial engineering applications, although the material will be relevant to those interested in applying Monte Carlo methods in other areas. The course will be aimed at risk managers, quantitative analysts and others who want to learn how to make use of Monte Carlo and related techniques in their work. Participants will learn how to

* use Monte Carlo methods for accurate option pricing, hedging and risk management
* understand what the values produced by Monte Carlo computations mean and how much confidence should be placed in them in practice
* increase the efficiency of their Monte Carlo applications through variance reduction techniques and the use of quasi-Monte Carlo methods
* incorporate the latest developments into their current practice.

A basic familiarity with option pricing and risk management will be helpful, but not necessary, and no computer programming experience will be assumed. Prior to the course, participants will receive a guided reading list that will help them to gain the maximum benefit from the course; during the course there will be computer laboratory time giving the opportunity for practical and experiential application of the material, and participants will be provided with demonstration software that implements the techniques and which they will be able use on their own computers.

Schedule: 8:30-4:30
Lunch: 12:00-1:00

Amenities:
Muffins or bagels are served in the morning and lunch will be catered to the classroom at noon. Freshly baked cookies are offered in the afternoon. Complimentary coffee, tea, juice or soft drinks are available throughout the day. A fridge and microwave are also available.

DAY 1

Introduction and overview- applications of Monte Carlo

- option pricing and risk management

Monte Carlo fundamentals
- randomness and reliability
- working in high dimensions: multi-asset and path-wise simulations
- efficiency and implementation issues
- variance reduction: antithetic variates, control variates,importance sampling

Quasi-Monte Carlo methods
- advantages over traditional Monte Carlo
- low-discrepancy sequences: typical problems and how to avoid them
- randomized quasi-Monte Carlo

DAY 2

Computing greeks
- finite differences
- the likelihood ratio method
- the `smoking adjoints' approach of Giles and Glasserman
American options
- lower bound methods (Longstaff-Schwartz)
- dual methods for upper bounds
- applications to swing options and storage contracts Stochastic volatility, jump-diffusion and other processes
Risk management applications
- VaR and other risk measures
- variance reduction using delta-gamma

Registration: $1000 + GST

(a 10% discount will be offered for multiple registrations per company - please email ccameron@ucalgary.ca for more information or call the PIMS-UC office at 220-3941)

About the lecturer:

Dr. Tony Ware is an Associate Professor in the Department of Mathematics at the University of Calgary, and is Director of the Mathematical and Computational Finance Laboratory which works with various local companies including Nexen, TransAlta, Enmax, Louis Dreyfus Energy and Direct Energy. He serves on the board for the Calgary chapter of PRMIA. In 2007 he was a visiting fellow in the Mathematical Finance Group at the Oxford Centre for Industrial and Applied Mathematics. From 2004 to 2006 leave he was leader of the MITACS project `Modelling trading and risk in the market’, which involves researchers from five universities across Canada and works with companies from the financial services, banking, insurance and energy sectors.

Dr Ware received his D.Phil. in 1991 from Oxford University and since then has held academic positions in Oxford, Durham and Calgary. His research interests are in numerical analysis, computational finance and the mathematical modelling of energy markets.

In addition to teaching various courses in mathematical and computational finance at the University of Calgary, Dr. Ware teaches a course on the mathematical modelling of natural gas markets for the Oxford M.Sc. Programme in Mathematical Finance. In 2007 he also taught a short course on swing option pricing at the AMSI / MASCOS Industry Workshop: The mathematics of electricity supply and pricing in Queensland, Australia.