# MAT-61956 Financial Mathematics and Statistics, 5 cr

Juho Kanniainen

#### Lessons

 Implementation Period Person responsible Requirements MAT-61956 2019-01 2 - 3 Juho Kanniainen Exam and project work

#### Learning Outcomes

A solid understanding of the mathematical basis of financial derivative pricing models is essential for understanding phenomena and pricing and hedging options in banks and financial institutions. Mathematically and statistically, the main focus areas are i) stochastic calculus for asset price modeling and derivative pricing and ii) model estimation. Financially, the main focus is on the pricing of equity and FX derivatives, but also interest rate derivatives are briefly covered. After completing this course, the student - Understands the no-arbitrage principle in option pricing - Understands the main mathematical concepts in continuous-time finance, including Ito¿s lemma, martingale processes, Radon-Nikodym derivative, and Girsanov's theorem - Is familiar with continuous and discrete-time models and methods to price and hedge and options and other derivatives on equities, indexes, and currencies - Is familiar with LIBOR market model for interest rate derivatives - Is familiar with stochastic volatility models - Understands advanced Monte-Carlo methods with variance reduction techniques and can apply them - Can implement derivative pricing models with stochastic volatility in Matlab or in some other environment - Can calibrate option pricing models with stochastic volatility using option market data - Can estimate the GARCH volatility models with maximum likelihood estimation methods and time-series data - Understands the main results of recent scientific papers on the field

#### Content

 Content Core content Complementary knowledge Specialist knowledge 1. Arbitrage pricing 2. Derivative contracts in financial markets 3. Pricing with tree models 4. Stochastic processes for asset price modelling in continuous time 5. Ito calculus 6. Martingale approach to arbitrage theory 7. Girsanov¿s theorem 8. Derivative pricing and hedging in continuous time 9. LIBOR market model 10. Stochastic volatility in continuous time 11. GARCH models for stochastic volatility 12. Maximum likelihood estimation

#### Instructions for students on how to achieve the learning outcomes

The grade of the course is based on the final exam and project work.

#### Assessment scale:

Numerical evaluation scale (0-5)

#### Partial passing:

Completion parts must belong to the same implementation

#### Study material

 Type Name Author ISBN URL Additional information Examination material Book The Concept and Practice of Mathematical Finance Mark Joshi 978-0521823555 No

#### Prerequisites

 Course Mandatory/Advisable Description MAT-01500 Insinöörimatematiikka X 5 Mandatory 1 MAT-01510 Insinöörimatematiikka A 5 Mandatory 1 MAT-01520 Insinöörimatematiikka B 5 Mandatory 1 MAT-01530 Insinöörimatematiikka C 5 Mandatory 1 MAT-01560 Matematiikka 5 Mandatory 1 MAT-01566 Mathematics 5 Mandatory 1 MAT-02500 Todennäköisyyslaskenta Mandatory 1 MAT-02506 Probability Calculus Mandatory 1

1 . Alternative prerequisite.