Fixed-income securities, basic portfolio optimization, binomial method for options; Ito process and its applications in stock market, Black-Scholes equation and its solution; random numbers, transformation of random numbers and generating normal variates, Monte Carlo integration, pricing options by Monte Carlo simulation, variance reduction techniques, quasi-random numbers and quasi-Monte Carlo simulation; introduction to finite difference methods, explicit and implicit finite difference schemes, Crank-Nicolson method, free-boundary value problems for American options.

For further information see the academic catalog: IAM749

#### Learning Outcomes

Students are expected to gain, beside the theoretical concepts, programming skills that are related to option pricing as well as optimization.

#### Suggested Textbooks

- Uğur, Ö., An Introduction to Computational Finance, Imperial College Press, 2009.
- Brandimarte, P., Numerical Methods in Finance: A MATLAB-Based Introduction, John Wiley & Sons, Inc., 2002.
- Seydel, R., Tools for Computational Finance, Springer-Verlag, 2002.

#### Outline

- Fixed-Income Securities
- Portfolio Optimization
- Options, and the Binomial Model
- Stochastic Differential Equations
- Ito Processes and Applications in Stock Market
- The Black-Scholes Equation, derivation and the Greeks
- Random Numbers and Transformation of Random Variables
- Monte Carlo (MC) Integration and Option Pricing by MC simulation
- Variance Reduction Techniques
- Introduction to Partial Differential Equations (PDEs) and Finite Difference Methods
- An Explicit Method and An Implicit Method
- Crank-Nicolson Method
- Some Advanced Topics (includes quasi Monte Carlo Simulation and Free Boundary Value Problems)