ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 20 Interactive Classroom: 15 Total: 125
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
It is intended that the student acquires basic knowledge of Financial Mathematics and its connection with the most recent models of Econometrics that take into account the important component of volatility. The course consists of two parts. The first is dedicated to the valuation of financial assets taught by Professor César Sánchez Sellero. The second is dedicated to volatility modelling by Professor Pedro Galeano San Miguel.
Part One. Asset valuation models
1. Introduction to Financial Engineering
1.1 Financial markets and products
1.2 Principles governing the functioning of financial markets: no arbitrage, risk aversion.
1.3 Objectives of Financial Engineering: Asset Valuation, Portfolio Design and Risk Management.
2. Deterministic Cash Flows
2.1 Cash Flow Concept
2.2 Simple and compound interest rates
2.3 Application of the principle of non-arbitrage
2.4 Present value and future value
2.5 Internal rate of return
2.6 Investment Evaluation
2.7 Regular payments: annuities
3. Random Cash Flows: Portfolio Management
3.1 Random Cash Flows
3.2 Credit sales
3.3 Performance of an asset and portfolio
3.4 Mean Diagram - Standard Deviation
3.5 Efficient Frontier Calculation
3.6 Inclusion of a risk-free asset and calculation of the efficient fund
4. Financial Asset Valuation Models (CAPM)
4.1 Introduction
4.2 The Efficient Fund as a Market Balancing Solution
4.3 The Asset Valuation Model (CAPM)
4.4 Evaluating an Investment Portfolio
4.5 The CAPM model as a valuation formula
5. Forwards, swaps and futures
5.1 Introduction to Financial Derivatives
5.2 Forward contracts
5.3 Exchanges
5.4 Futures
6. Evaluating Options: The Binomial Model
6.1 Types of Options: Call Options, Put Options, European Options, and American Options.
6.2 Value of an Option at Expiry
6.3 Parity between the values of call and put options
6.4 Binomial model of asset price developments
6.5 Valuing Options in a Binomial Model
6.6. Building a binomial model
7. Evaluating Options: The Black-Scholes Model
7.1 Introduction
7.2 Stochastic Models: Random Walks, Brownian Motion, and Stochastic Differential Equations
7.3 The Black-Scholes model
7.4 Options valuation under the Black-Scholes model
Part Two. Financial Time Series
1. Introduction to Financial Time Series
1.1 Introduction
1.2 Financial returns and their statistical properties
1.3 Empirical characteristics of financial returns
2. Conditional Heteroscedastic Models
2.1 Introduction
2.2 The main structure of volatility models
2.3 Conditional heteroscedastic models
3. Higher-Order Moments
3.1 Introduction
3.2 Modelling higher-order moments
3.3 Near-maximum likelihood estimation
3.4 Alternative distributions
4. Value at Risk
4.1 Introduction
4.2 Value at Risk
4.2 Value-at-risk calculation
4.3 Alternative approaches
5. Multivariate Volatility Models
5.1 Introduction
5.2 General Structure of Multivariate Volatility Models
5.3 Multivariate extensions of the univariate GARCH model
5.4 Conditional correlation models
5.5 Alternative models
6. Portfolio Optimization
6.1 Introduction
6.2 Portfolio Selection
BASIC BIBLIOGRAPHY
Luenberger, D. (2013). Investment science. Oxford University Press.
Tsay, R.S. (2010): "Analysis of Financial Time Series". (Third edition) John Willey & Sons. New York.
COMPLEMENTARY BIBLIOGRAPHY
Andersen,T.G., Davis, R.A., Kreiss, J-P y Mikosh, T.(editores) (2009). "Handbook of financial time series". Springer
Chan, N.H. (2002): "Time Series. Applications to Finance". John Willey & Sons. New York.
Díaz de Castro, L. y Mascareñas, J. (1998): "Ingeniería Financiera. La gestión en los mercados financieros internacionales". Segunda edición. McGraw-Hill
Fan, J. y Yao, Q. (2003): "Nonlinear Time Series. Nonparametric and Parametric Methods".
Fernández, P. (1996): "Opciones, futuros e instrumentos derivados". Ediciones Deusto
Franses, P.H. y Dijk, D.V. (2000): “Non-linear Time Series Models in Empirical Finance”. Cambridge University Press. Cambridge.
Gourieroux, C. (1997): "ARCH Models and Financial Applications". Springer-Verlag. New York, Inc. New York.
Gourieroux, C. y Jasiak, J. (2001): "Financial Econometrics". Princeton University Press. Princeton, New Jersey.
Neftci, S.N. (2008). Principles of financial engineering. Academic Press.
Ruppert, D. (2004): "Statistics and Finance. An Introduction". Springer-Verlag. New York.
Steele, J.M. (2001). Stochastic calculus and financial applications. Springer.
Trivedi, P.K. y Zimmer, D.M. (2005): "Copula Modelling: An Introduction to Practitioners". Foundations and Trends in Econometrics. Vol. 1, 1, pg. 1-111.
Basic and general competencies
In relation to basic competencies, students are expected to know how to apply their knowledge to various cross-curricular environments, to know how to prepare appropriate reports and to have the ability to communicate conclusions (CB7, CB8 and CB9).
In terms of general skills, it is intended that students have the ability to solve the algorithms developed in the subject, to present them well, to work in a team and to be able to start certain research tasks.
Transversal competencies
In relation to transversal skills, it is intended that the student has a certain ability to identify and model real-life problems that motivate the possible application of the methodology developed, scientific communication, planning, interpretation and dissemination of the results obtained. (T1, T2, T7 and T9)
Specific competencies
The student will acquire knowledge about asset valuation and management with the associated stochastic differential equations. You will acquire the ability to analyse financial series and model volatility.
The teaching of the first part will consist of the presentation of the asset valuation models and the resolution of exercises related to these models. The teaching of the second part will consist of the presentation of the econometric models of financial series, as well as the resolution of practical examples. Professor Wenceslao González Manteiga will evaluate the works proposed by Professor Pedro Galeano.
The final grade will proceed to 100% of the continuous assessment, with the first part of the subject constituting 50% of the assessment and the second part the other 50%.
For the first part of the contents, a written control will be carried out in the classroom during the teaching period, which will contribute 40% of the score of this part of the subject, and also a written work with the resolution of exercises on the valuation of financial assets, which will contribute the other 60%. The evaluation of the resolution of exercises aims to check the acquisition of several specific competencies.
The evaluation of the second part of the course will consist of the application of the econometric models of financial series to real data. In the evaluation of the second part, it is intended to analyse, in addition to the specific competences acquired, those others that have to do with practically all the various competences, with the resolution on a real database, with a group analysis and with the presentation and defence of what has been done in public.
Face-to-face teaching: 35 hours of lectures and practices in solving exercises and modelling practical examples.
Study and personal work: 50 h.
It is advisable to have some familiarity with basic statistical concepts, particularly with Box-Jenkins regression and time series models. Although it is not essential, it is also helpful to have some knowledge of stochastic processes.
The development of the contents of the subject will be carried out taking into account that the competencies to be acquired by the students must comply with the MECES3 level. This course will have a large practical component, with an emphasis on the identification and modelling of complex and highly specialised real problems in relation to Financial Engineering.
In cases of fraudulent completion of exercises or tests, the provisions of the respective regulations of the universities participating in the Master's Degree in Statistical Techniques will apply.
This guide and the criteria and methodologies described in it are subject to modifications derived from the regulations and guidelines of the universities participating in the Master's Degree in Statistical Techniques.
Wenceslao Gonzalez Manteiga
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813204
- wenceslao.gonzalez [at] usc.es
- Category
- Professor: University Professor
Cesar Andres Sanchez Sellero
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813208
- cesar.sanchez [at] usc.es
- Category
- Professor: University Lecturer
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| 06.25.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 04 |