# Events/Masterclasses

### From Thalesians

# Introduction

You may already be familiar with the highly successful Thalesian seminar series and may have attended one of our workshops. These events serve to bring members of the quantitative and computational finance community together to exchange ideas, learn from each other, and perhaps even create something new.

We are delighted to announce the Thalesian **masterclasses**. These events are fundamentally different from both the workshops and seminars. Their purpose is to bring together a small class of students — typically experienced practitioners or postgraduates, but we shall also offer introductory courses — and a world-class expert in a particular field. Hence the name: *master-classes*.

These classes will consist of (very intensive!) lectures and tutorials. The students are expected to work very hard. This is a small price to pay for an unparalleled learning experience and an opportunity to ask a master of the subject your most challenging questions.

As always we are committed to making quantitative finance affordable for all. You excel through your intellectual curiosity, your ability, and hard work; not by paying a lot of money! This commitment is reflected in the surprisingly low costs.

Because we aim to keep our classes reasonably small, places will be strictly limited. Please reserve your place early to avoid disappointment. You can register online. If you have any questions, please send them to `info`, which is `at thalesians dot com`.

We look forward to seeing you at one of our masterclasses!

# Previous Masterclasses

## Thalesian Masterclass — Dr Patrick S. Hagan, Head, Quantitative Analytics, Chief Investment Office, JP Morgan — Managing Smile Risk and Exotics

### Format

Two three hour lectures over two consecutive days.

### Schedule

There are a limited number of places on this course, so we strongly urge you to register on *Meetup.com* as soon as you can. The two days are complementary: the first is a lecture covering the fundamentals of volatility models for managing smile risk. The second day covers the practical issues of IR modeling and how they are used to manage risk on exotics books.

#### Day 1: Lecture

##### Managing smile risk

Starting with Black's model, we analyse the local volatility, stochastic volatility, and finally Levy-flight based models, exploring how each succeeding model gives better management of the risks inherent in our vanilla interest rate books.

##### Date and Time

6:00 p.m. — 9:00 p.m. on Wednesday, 3rd November, 2010.

#### Day 2: Lecture

##### Managing exotics

We look at the risks inherent to exotic rates books and the types of interest rate models available to manage them. We then examine how the IR models are used in practice: selection of the set of calibration instruments, calibration of the IR model and pricing of the exotics. We then look at how this procedure generates the risks and hedges of the exotic deals, which leads to improved methods for selecting effective models and calibration methods. Finally we look at risk migration methods (adjusters), and how they can be used to provide more effective hedges.

##### Date and Time

6:00 p.m. — 9:00 p.m. on Thursday, 4th November, 2010.

#### Cost

**199 GBP.**

#### *Meetup.com*

You can register for this event and pay online on *Meetup.com*: http://www.meetup.com/thalesians/calendar/14666429

#### Venue

MWB Canary Wharf, Level 33, 25 Canada Square, E14 5LQ, London, UK.

### Speaker

**Patrick Hagan** has made several fundamental contributions to mathematical finance, particularly in the area of interest rate derivatives modelling, where he pioneered the SABR volatility model - now the de-facto approach for including stochastic volatility within the LIBOR market model. Patrick Hagan received his Ph.D and B.S in Applied Mathematics from Caltech. Over the years he has worked at Bloomberg and several banks designing trading systems for fixed income, credit, and foreign exchange derivatives, as well as developing the component models, calibration methods, and numerical algorithms. He served at Head of Quantitative Analytics and Chief Investment Officer at JP Morgan. Before entering finance he was Deputy Director of the CNLS and a member of the Computer Research and Applications group at Los Alamos National Laboratory. He has also worked at Exxon Science Laboratories, and has taught at Caltech, Stanford, the Institute for Mathematics and its Applications, and NYU.

### Prerequisites

We will assume that the audience has a solid grasp of basic stochastic calculus and mathematical finance and is aware of the essential principles of interest rate modeling and the complex issues arising in the practical application of financial derivative pricing theory.

### Objectives

Attendees of the two-day tutorial should expect to accomplish the following:

- Learn about the different types of volatility models used in interest rate derivative modeling
- Understand the implications of each volatility modelling approach on the management of smile risk
- Discover how to, at least roughly, build a pricing/hedging/risk management system
- Gain insight into how to calibrate interest rate models with exotic instruments
- Understand how exotic instrument risk and hedging enable the selection of improved models and calibration procedures
- Find out about risk migration methods and how they improve hedging

### Bibliography

- Patrick S. Hagan, Deep Kumar, Andrew S. Lesniewski and Diana E. Woodward, Managing Smile Risk, Wilmott Magazine, Feb 2002, http://www.wilmott.com/pdfs/021118_smile.pdf
- Patrick S. Hagan, Adjusters: Turning Good Prices into Great Prices, August 2002, http://www.wilmott.com/pdfs/030813_hagan.pdf

### Resources

- NYU course notes on interest rate and credit models: http://www.math.nyu.edu/~alberts/spring07/index.html
- Venue details: http://meetingvenues.mwbex.com/meeting-room/CanaryWharf.html

## Thalesian Masterclass — Dr. Dan Crisan — Introduction to Stochastic Calculus

### Format

A lecture and a tutorial, six hours over two days.

### Schedule

Due to limited places, we strongly recommend that you register for this two-day event on *Meetup.com* as soon as possible. The two days are complementary: the first is a Lecture, covering the theory, the second is a Tutorial, allowing you to practice and ask questions.

#### Day 1: Lecture

##### Date and Time

6:00 p.m. — 9:00 p.m. on Thursday, 7th October, 2010.

#### Day 2: Tutorial

##### Date and Time

6:00 p.m. — 9:00 p.m. on Friday, 8th October, 2010.

#### Venue

MWB Canary Wharf, Level 33, 25 Canada Square, E14 5LQ, London, UK.

#### Cost

**£199 only, all-inclusive**

#### *Meetup.com*

You can register for this event and pay online on *Meetup.com*: http://www.meetup.com/thalesians/calendar/14070200/

### Abstract

As Baxter and Rennie put it in their celebrated book (see [1]), the rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. This statement was true in the early nineties and it is even more so at the end of the noughties. It is the aim of this course to provide a rigorous and accessible account of the advanced mathematics required for making such decisions. More precisely, the course will cover the fundamentals of stochastic calculus with financial applications in mind. The focal point of the course is the introduction of the Itō integral with Brownian motion as an integrator and its many consequences, including the martingale representation theorem and the fundamental theorem of Cameron, Martin and Girsanov and its applications to finance.

### Lecturer

**Dan Crisan** is a Professor in Mathematics at Imperial College London. His expertise lies in the area of Stochastic Analysis with applications in Engineering and Finance. His current research is on developing high-order numerical algorithms for solving stochastic differential equations, approximating schemes for backward SDEs and particle methods for nonlinear filtering. His book, Fundamentals of Stochastic Filtering appeared at Springer Verlag at the begining of the year and he is currently involved in editing an advanced handbook on Nonlinear Filtering to be published by the Oxford University Press. Dr. Crisan is a member of the editorial board of the Journal of Mathematics and Computation. He is also actively involved in teaching. Among numerous other courses, he has taught stochastic filtering, numerical stochastics, and measure-valued processes at Imperial College; applied probability, and stochastic calculus and applications at Cambridge University.

### Prerequisites

We will assume that the audience is familiar with basic probability theory, measure theory and calculus.

### Syllabus

We aim to cover the following:

- Continuous processes
- General properties
- Martingales in continuous time
- Doob-Meyer decomposition

- Brownian motion
- Definition and construction from discrete time processes.
- Properties of the Brownian paths.
- Brownian motion as a model for stock price evolution.

- Stochastic calculus
- Construction of the Itō integral
- Change of Variable formula (Itō’s rule)
- Integration by parts formula
- The martingale representation theorem

- Stochastic differential equations (SDEs)
- Formulation
- Existence and uniqueness results
- Elementary properties of solutions
- Examples

### Bibliography

- Baxter, Martin; Rennie, Andrew. Financial Calculus : An Introduction to Derivative Pricing. Cambridge University Press, Cambridge, 1996.
- Lamberton, Damien; Lapeyre, Bernard. Introduction to stochastic calculus applied to finance. Second edition. CRC Financial Mathematics Series. Chapman and Hall, 2008.
- Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991.
- Øksendal, Bernt. Stochastic differential equations. An introduction with applications. Sixth edition. Universitext. Springer-Verlag, Berlin, 2003. xxiv+360 pp.
- Williams, David. Probability with martingales. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge, 1991.
- Kloeden Peter, Platen Ekhart, Numerical solution of stochastic differential equations. Springer-Verlag, Berlin, 1999.

### Resources

- Dr. Dan Crisan's home page: http://www.ma.ic.ac.uk/~dcrisan/
- Dr. Dan Crisan in Imperial College Directory: http://www3.imperial.ac.uk/people/d.crisan
- Venue details: http://meetingvenues.mwbex.com/meeting-room/CanaryWharf.html

## Thalesian Masterclass — Dr. Dan Crisan — Introduction to Stochastic Calculus

### Format

A lecture and a tutorial, six hours over two days.

### Schedule

Although we strongly recommend you to register for both days, you can register for them individually. The two days are complementary: the first is a Lecture, covering the theory, the second is a Tutorial, allowing you to practice and ask questions. If you intend to attend both, you should register for both individually on *Meetup.com*.

#### Day 1: Lecture

##### Date and Time

6:00 p.m. — 9:00 p.m. on Monday, 15th March, 2010.

##### Venue

MWB Canary Wharf, Level 33, 25 Canada Square, E14 5LQ, London, UK.

##### Cost

**£199 only, all-inclusive**

##### *Meetup.com*

You can register for this event and pay online on *Meetup.com*: http://www.meetup.com/thalesians/calendar/12174631/

#### Day 2: Tutorial

##### Date and Time

6:00 p.m. — 9:00 p.m. on Tuesday, 16th March, 2010.

##### Venue

MWB Canary Wharf, Level 33, 25 Canada Square, E14 5LQ, London, UK.

##### Cost

**£99 only, all-inclusive**

##### *Meetup.com*

You can register for this event and pay online on *Meetup.com*: http://www.meetup.com/thalesians/calendar/12174649/

### Abstract

As Baxter and Rennie put in in their celebrated book (see [1]), the rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. This statement was true in the early nineties and it is even more so at the end of the noughties. It is the aim of this course to provide a rigorous and accessible account of the advanced mathematics required for making such decisions. More precisely, the course will cover the fundamentals of stochastic calculus with financial applications in mind. The focal point of the course is the introduction of the Itō integral with Brownian motion as an integrator and its many consequences, including the martingale representation theorem and the fundamental theorem of Cameron, Martin and Girsanov and its applications to finance.

### Lecturer

**Dan Crisan** is a Professor in Mathematics at Imperial College London. His expertise lies in the area of Stochastic Analysis with applications in Engineering and Finance. His current research is on developing high-order numerical algorithms for solving stochastic differential equations, approximating schemes for backward SDEs and particle methods for nonlinear filtering. His book, Fundamentals of Stochastic Filtering appeared at Springer Verlag at the begining of the year and he is currently involved in editing an advanced handbook on Nonlinear Filtering to be published by the Oxford University Press. Dr. Crisan is a member of the editorial board of the Journal of Mathematics and Computation. He is also actively involved in teaching. Among numerous other courses, he has taught stochastic filtering, numerical stochastics, and measure-valued processes at Imperial College; applied probability, and stochastic calculus and applications at Cambridge University.

### Prerequisites

We will assume that the audience is familiar with basic probability theory, measure theory and calculus.

### Syllabus

We aim to cover the following:

- Continuous processes
- General properties
- Martingales in continuous time
- Doob-Meyer decomposition

- Brownian motion
- Definition and construction from discrete time processes.
- Properties of the Brownian paths.
- Brownian motion as a model for stock price evolution.

- Stochastic calculus
- Construction of the Itō integral
- Change of Variable formula (Itō’s rule)
- Integration by parts formula
- The martingale representation theorem

- Stochastic differential equations (SDEs)
- Formulation
- Existence and uniqueness results
- Elementary properties of solutions
- Examples

### Bibliography

- Baxter, Martin; Rennie, Andrew. Financial Calculus : An Introduction to Derivative Pricing. Cambridge University Press, Cambridge, 1996.
- Lamberton, Damien; Lapeyre, Bernard. Introduction to stochastic calculus applied to finance. Second edition. CRC Financial Mathematics Series. Chapman and Hall, 2008.
- Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus. Second edition. Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991.
- Øksendal, Bernt. Stochastic differential equations. An introduction with applications. Sixth edition. Universitext. Springer-Verlag, Berlin, 2003. xxiv+360 pp.
- Williams, David. Probability with martingales. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge, 1991.
- Kloeden Peter, Platen Ekhart, Numerical solution of stochastic differential equations. Springer-Verlag, Berlin, 1999.

### Resources

- Dr. Dan Crisan's home page: http://www.ma.ic.ac.uk/~dcrisan/
- Dr. Dan Crisan in Imperial College Directory: http://www3.imperial.ac.uk/people/d.crisan
- Venue details: http://meetingvenues.mwbex.com/meeting-room/CanaryWharf.html

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