Monte Carlo Methods in Financeby Prof. Dr. Alberto SuarezUniversidad Autonoma de Madrid Learn how to measure the risk of an investment portfolio!In this course you will simulate the time evolution of prices of financial assets, use the Bla…

Monte Carlo Methods in Finance

Universidad Autónoma de Madrid

Learn how to measure the risk of an investment portfolio!

In this course you will simulate the time evolution of prices of financial assets, use the Black-Scholes model to price European or Asian options and compute the Value-at-Risk of a portfolio. The approach is hands-on with a strong emphasis on practical simulations that you will program, run and explore in your own computer.

"Monte Carlo Methods in Finance" will be offered on iversity, starting 20 January 2014.

Course Structure

The course is structured in 9 one or two-week chapters

Chapter 1: Introduction Chapter 2: Understanding random numbers Chapter 3: Generating random numbers Chapter 4: Brownian motion Chapter 5: Ordinary differential equations Chapter 6: Stochastic differential equations Chapter 7: Pricing of simple derivative products Chapter 8: Pricing of more complex derivative products Chapter 9: Modeling and quantifying financial risk

Chapters are divided into units. Each unit consists of a video followed by a multiple choice question. At the end of each chapter, you will solve and turn in some homework exercises. These exercises will be evaluated by peer grading.

Some of the explanations in the videos and the exercises make reference to short programs that you can download and execute in your own computer. You are encouraged to experiment with these programs (modify the values of parameters, complete or rewrite the code to alter the model or to implement related functionality) and run your own simulations. The code provided can be executed in either GNU Octave or MATLAB.

Learning objectives

At the end of this course you will know how to answer the following questions:

Why are random numbers needed in quantitative finance? And, if they are random, how can they be used to give precise, accurate answers to quantitative financial problems?

What is the Black-Scholes model and how can it be used to simulate the evolution of asset prices in financial markets?

How are Monte Carlo methods used to determine the right price of a derivative product, such as a European call option?

What is the theory of copulas and how can it be used to model general dependencies among financial assets?

How is financial risk modeled, characterized and quantified?

Workload

You will need between 5 and 8 hours of work per week during a total of 12 weeks to complete all the learning activities, including the homework.

Prior knowledge

The course is geared to students not only in economics and finance, but also in mathematics, computer science, engineering, physics and the natural sciences.

No knowledge of finance is required.

Basic knowledge of Calculus (integration and differentiation, Taylor series), Linear Algebra (matrices, determinants, eigenvalues and eigenvectors) and Probability (random variables, probability density and cumulative distribution functions) at an introductory undergraduate level is strongly recommended.

Programming knowledge is recommended. We will be designing simulations that can be executed in either GNU Octave or in Matlab. The programs will be short, intuitive, fully documented and easy to follow. Yet they will be powerful tools under your control, and will allow you to explore, experiment and learn at your own initiative.

Timeline

The course is scheduled to start on 20 January 2014. There will be a short break for Easter.

Language

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