| Study programme competencies |
| Code | Study programme competences |
| A1 | Alcanzar un conocimiento básico en un área de Ingeniería/Ciencias Aplicadas, como punto de partida para un adecuado modelado matemático, tanto en contextos bien establecidos como en entornos nuevos o poco conocidos dentro de contextos más amplios y multidisciplinares. |
| A2 | Modelar ingredientes específicos y realizar las simplificaciones adecuadas en el modelo que faciliten su tratamiento numérico, manteniendo el grado de precisión, de acuerdo con requisitos previamente establecidos. |
| A3 | Determinar si un modelo de un proceso está bien planteado matemáticamente y bien formulado desde el punto de vista físico. |
| A4 | Ser capaz de seleccionar un conjunto de técnicas numéricas, lenguajes y herramientas informáticas, adecuadas para resolver un modelo matemático. |
| A5 | Ser capaz de validar e interpretar los resultados obtenidos, comparando con visualizaciones, medidas experimentales y/o requisitos funcionales del correspondiente sistema físico/de ingeniería. |
| A6 | Ser capaz de extraer, empleando diferentes técnicas analíticas, información tanto cualitativa como cuantitativa de los modelos. |
| A7 | Saber modelar elementos y sistemas complejos o en campos poco establecidos, que conduzcan a problemas bien planteados/formulados. |
| A8 | Saber adaptar, modificar e implementar herramientas de software de simulación numérica. |
| B1 | Saber aplicar los conocimientos adquiridos y su capacidad de resolución de problemas en entornos nuevos o poco conocidos dentro de contextos más amplios, incluyendo la capacidad de integrarse en equipos multidisciplinares de I+D+i en el entorno empresarial. |
| B2 | Poseer conocimientos que aporten una base u oportunidad de ser originales en el desarrollo y/o aplicación de ideas, a menudo en un contexto de investigación, sabiendo traducir necesidades industriales en términos de proyectos de I+D+i en el campo de la Matemática Industrial |
| B3 | Ser capaz de integrar conocimientos para enfrentarse a la formulación de juicios a partir de información que, aun siendo incompleta o limitada, incluya reflexiones sobre las responsabilidades sociales y éticas vinculadas a la aplicación de sus conocimientos. |
| B4 | Saber comunicar las conclusiones, junto con los conocimientos y razones últimas que las sustentan, a públicos especializados y no especializados de un modo claro y sin ambigüedades. |
| B5 | Poseer las habilidades de aprendizaje que les permitan continuar estudiando de un modo que habrá de ser en gran medida autodirigido o autónomo, y poder emprender con éxito estudios de doctorado. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Knowledge of the management of the most popular financial products, specially options and bonds | AC1 AC2 AC5 AC6 AC7 |
BJ1 BC3 BR1 |
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| Knowledge and application of the usual techniques of stochastic calculus to solve the pricing problems | AC2 AC6 AC7 |
BJ1 BR1 |
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| Knowledge of the dynamic hedging methodology to pose Black-Scholes mathematical models | AC2 AC3 AC7 |
BJ1 BC1 BR1 |
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| For a given financial derivative, ability to pose the most suitable Black-Scholes pricing model | AC1 AC2 AC4 AC7 |
BC1 BC2 BC3 BR1 |
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| Knowledge of the most suitable numerical methods to solve the Balck-Scholes models for the different financial products, either with one or two stochastic factors. | AC4 AC5 AC8 |
BC1 BC2 BC3 BR1 |
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| Knowledge about models of financial risk and the associated computations | AC1 AC2 AC5 AC6 AC7 |
BJ1 BC1 BC2 BC3 BR1 |
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| Contents |
| Topic | Sub-topic |
| 1. Financial markets and financial derivatives | |
| 2. Discounted value of riskless financial products | |
| 3. Pricing models for risky assets | |
| 4. Dynamic hedging methodologies and Black Scholes models | |
| 5. Black-Scholes models for options and bonds with one stochastic factor | |
| 6. Black-Scholes models for options and bonds with two stochastic factors |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Problem solving | A2 A3 A4 A5 A6 A7 B5 B3 B1 | 0 | 60 | 60 |
| Problem solving | A2 A3 A4 A5 A6 A7 B5 B3 B1 | 0 | 36 | 36 |
| Objective test | A2 A3 A6 A7 B5 | 4 | 0 | 4 |
| Guest lecture / keynote speech | A1 A2 A3 A4 A5 A6 A7 A8 B2 B5 B3 B1 B4 | 42 | 0 | 42 |
| Personalized attention | 8 | 0 | 8 | |
| (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||
| Methodologies |
| Methodologies | Description |
| Problem solving | A set of problems is delivered to the student, some of them shorter to understand and practice concepts and technique, others are more complex. |
| Problem solving | - In the .pdf documents exhibited during lectures the are some easy exercises to review and apply the explained concepts - Moreover, some bibliographic references are indicated that contain exercises related to the developed subject |
| Objective test | Several problems are posed to be solved by the student who can use the slides containing the explanations in the lectures |
| Guest lecture / keynote speech | - Previously to lecture sessions, a .pdf document with the slides to use in the lecture is delivered to students - Table PC and videoconference facilities will be used so that lectures can be followed by the students from the different campus - Paricipation of students with quetions and comments will be encouraged. Questions will be solved and comments will be illustrated by means of Windows Journal computer application |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Objective test | A2 A3 A6 A7 B5 | A written exam of practical applications of the lectured contents will take place in a fixed date. In case of failing, a recovery exam will take place in a later fixed date | 60 |
| Problem solving | A2 A3 A4 A5 A6 A7 B5 B3 B1 | A set of exercises proposed to be solved outside classroom timetable will be evaluated | 40 |
| Assessment comments | |||
| Sources of information |
| Basic |
C. Vázquez (2010). An introduction to Black-Scholes modeling and numerical methods in derivatives pricing. MAT Serie A
I. Achdou, O. Pironneau (2005). Computational methods for options pricing. SIAM
T.Mikosch (1998). Elementary Stochastic Calculus with Finance in View. World Scientific, (Singapur)
P.G.Zhang (1998). Exotic Options, A guide to second generation option. World Scientific (Singapur)
C.W. Oosterlee, L.Grzelak (2020). Mathematical modeling and computation in finance. World Scientific (london)
P.Wilmott, S.Howison, J.Dewynne (1996). Option Pricing: Mathematical Models and Computation. Oxford Financial Press
J.C.Hull (2000). Options, Futures and Other Derivatives. Prentice-Hall Inc., (New Jersey)
A. Pascucci (2011). PDE and martingale methods in option pricing. Bocconi University Press, Springer
P.Wilmott, S.Howison, J.Dewynne (1996). The mathematics of Financial Derivatives, A Student Introduction. Cambridge University Press
R.Seydel (2007). Tools for Computational Finance. Universiteitext, Springer-Verlag |
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| Complementary | |
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| Recommendations | |
| Subjects that it is recommended to have taken before | |
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| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus | |
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| Other comments | |