Many problems in economics, finance and financial engineering do not possess a closed-form solution which could be computed easily. Typically, these problems are solved by using numerical algorithms and simulation methods. This course covers the study and implementation of such techniques. These include Monte Carlo simulation for pricing complex derivatives; finite difference methods to solve partial differential equations for option pricing; effective methods to compute hedging strategies; numerical dynamic programming for optimal portfolios, resource management and economic growth. Advanced understanding of these techniques and their implementation on computer using software packages and programming languages is the focus of this course.

One two-hour lecture per week for 10 weeks.

Ten one-hour computer labs.

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The main aim of this course is to introduce students to core techniques in computational finance, such as simulation of asset prices, pricing options using stochastic models, Monte Carlo methods as applied to complex derivatives, solving Black-Scholes type equations numerically, solving dynamic optimization problems numerically, and how to implement these techniques using modelling software packages and programming languages.

By the end of this course students will be able to:

1. Calculate the price and hedging portfolios of complex derivatives using Monte Carlo simulations 

2. Calculate the price of American and other exotic options by implementing numerical methods to solve the related partial differential equations

3. Implement dynamic programming algorithms to solve problems in portfolio optimisation, resource management and monetary policy

4. Demonstrate advanced skills in modelling software packages and programming languages

Students must submit at least 75% by weight of the components (including quizzes and examination) of the course's summative assessment.