Course guide of Introduction to Financial Operations (2351114)

Not required

• Basic concepts: financial capital and operation.
• Classic financial theorems.
• Short-term operations.
• Annuity Theory.
• Constitution and amortization: dynamics and effective interest rate.

The objective of this program is to provide the student with an overview of the basic concepts of Financial Mathematics.

More specifically, the student:

• will understand the simple financial theorem and will applicate it to short-term operations.
• will understand the compound and continuous financial theorems.
• will know how to identify and value an annuity.
• will understand the concepts of loan and obligation and calculate the magnitudes related to them.

Topic 1. Basic concepts.

1. Financial Capital.
2. Financial Theorem. Properties.
3. Financial Operation.
4. Mathematical reserve or financial balance.
5. Commercial characteristics, effective interest rate and APR.
6. How interest rates are formed. The EURIBOR.

Topic 2. Simple interest.

1. Simple capitalization with due interest rate.
2. Simple discount with due interest rate or Rational Discount.
3. Simple discount with prepaid interest rate or Commercial Discount.
4. Change in units of measure: equivalent rates.
5. Substitution of capital: common maturity and average maturity.
6. Annex I: Simple capitalization with prepaid interest rate.
7. Annex II: Comparison of the different theorems.

Topic 3. Short-term operations.

1. Discount of bills of exchange.
2. Settlement of current savings accounts.
3. Settlement of current credit accounts.
4. Market operations:
   1. Spot purchase-sale.
   2. Forward purchase-sale.
   3. Operations with repurchase agreement (REPO).

Topic 4. Compound and continuous theorems.

1. Compound capitalization with due interest rate.
2. Compound discount with due interest rate.
3. Change in units of measure: equivalent rates.
4. Effective and nominal interest rate.
5. Continuous capitalization and discount.
6. Application of compound and continuous theorems.
7. Annex I: Compound capitalization and discount with prepaid interest rate.
8. Annex II: Comparison between the different theorems.

Topic 5. Valuation of annuities.

1. What is an annuity? Types of annuities.
2. Value of an annuity: present and future values.
3. Constant progressions: ordinary and perpetuity.
4. Geometric progressions: ordinary and perpetuity.
5. Arithmetic progressions: ordinary and perpetuity.
6. Fractional progressions.
7. Examples. Constitution of a capital through an annuity.

Topic 6. Loans.

1. What is a loan?
2. Evolution of a loan.
3. Amortization systems.

   1. Periodic payment of interest.

   2. French system.

   3. Constant repayment amortization.

4. Floating interest rate loans.
5. Grace period and cancellation in a loan.
6. Commercial characteristics: Effective interest rate and TAE.
7. Amortized Cost.
8. Annex I: Amortization with Geometric or Arithmetic payments.
9. Annex II: Sinking Fund and German System.

The theory program is complemented by the practical program.

Frías-Aceituno, J.V. (2024). Introducción Operaciones Financieras. Editorial: Técnica Avicam.

CAPINSKI, M., & ZASTAWNIAK, T. (2003). Mathematics for finance: an introduction to financial engineering (1st ed. 2003). Springer London. https://doi.org/10.1007/b97511

LOVELOCK. D., MENDEL, M. & WRIGHT, A.L. (2007). An Introduction of he Mathematics of Money. Saving and Investing (1st ed. 2000). Springer New York. ISBN: 978-0387-34432-4.

PETTERS, A. O., & DONG, X. (2016). An Introduction to Mathematical Finance with Applications: Understanding and Building Financial Intuition (1st ed. 2016). Springer New York. https://doi.org/10.1007/978-1-4939-3783-7

POLLARD, A. H. (1977). An introduction to the mathematics of finance (Second edition). Pergamon Press.

ALEGRE ESCOLANO, P. y otros. (1989): Ejercicios resueltos de matemática de las operaciones financieras. Ediciones AC.

ALEGRE ESCOLANO, P. y otros. (1997): Curso interactivo de matemática financiera. Editorial McGrawHill.

BONILLA, M.; IVARS, A.; MOYA, I. (2006): Matemática de las Operaciones Financieras: teoría y práctica. Editorial Thomson.

DE PABLO, A. (1994): Unidades didácticas de matemáticas de las operaciones financieras. UNED.

GARCÍA BOZA, J. (2002): Problemas resueltos de matemática de las operaciones financieras, Ed. Pirámide, Madrid.

GARCÍA BOZA, JUAN (2011). Matemáticas Financieras. Editorial: Pirámide.

GIL PELAEZ, L. (1987): Matemática de las operaciones financieras. Editorial AC.

GIL PELAEZ, L. (1987): Matemática de las operaciones financieras: problemas resueltos. Editorial AC.

GONZÁLEZ CATALÁ, V. (1992): Análisis de las Operaciones Financieras, Bancarias y Bursátiles. Ciencias Sociales, Madrid.

GONZÁLEZ CATALÁ, V. (1999): Operaciones Financieras, Bancarias y Bursátiles. Curso práctico. Ciencias Sociales, Madrid.

MENEU, V.M.; JORDÁ, M.P.; BARREIRA, M.T. (1994): Operaciones Financieras en el Mercado Español. Editorial Ariel Economía.

RODRIGUEZ RODRÍGUEZ, A. (1984): Matemática de la financiación. Romagraf. S.A.

TOVAR JIMENÉZ, JOSÉ (2ªedición): Operaciones Financieras (Teoría y Problemas Resueltos). Editorial CEF.

• European Central Bank
• Tesoro público
• Banco de España
• Financial Times
• Invertia. El Español

• MD01. Docencia presencial en el aula 
• MD02. Estudio individualizado del alumno, búsqueda, consulta y tratamiento de información, resolución de problemas y casos prácticos, y realización de trabajos y exposiciones. 
• MD03. Tutorías individuales y/o colectivas y evaluación  

The preferred system will be the continuous assessment system. However, a single final assessment could be applied when students cannot comply with the continuous evaluation method for working reasons, health status, disability, mobility programs or any other justified cause. The student may request the single final assessment in accordance with the Student Assessment and Grading Regulations (art. 8).

The continuous assessment system is based on:

• A partial exam, corresponding to the first four topics, that will suppose a 40% of the final grade for the subject. This exam will consist of two parts: theory and practice. Each of them will have a maximum score of 10 points. Theory will be weighted at 30% (1.2 points), and theoretical-practical, at 70% (2.8 points). It is necessary to obtain at least a minimum of 3.5 points out of 10 points in each of these parts (theory -0.42 points- and theoretical-practical -0.98 points-). Otherwise, the grade will be "Not Passed", and the student will have to take an exam of this part of the subject in the ordinary call (on the date set by the Center). Additionally, the student may choose to retake the partial exam, corresponding to the first four topics, waiving the grade obtained in the previous partial exam, on the day set in the examination calendar of the Center for the regular call of this subject. In this case, the grade obtained in this new exam will replace the one obtained previously.
  The theoretical part will consist of a series of multiple-choice questions with a single correct answer. Wrong answers score negatively (the penalty will be notified to the student), unanswered questions do not add or subtract. The practice will consist of solving exercises.

• A final exam, corresponding to the topics 5 and 6, to be taken on the official date set by the Center (ordinary call), which will suppose a 60% of the final grade for the subject. It will consist of two parts: theory and practice. Each of them will have a maximum score of 10 points. Theory will be weighted at 30% (1.8 points), and theoretical-practical, at 70% (4.2 points). It is necessary to obtain at least a minimum of 3.5 points out of 10 points in each of the exam parts (theory -0.63 points- and theoretical-practical -1.47 points-) to be able to add the grades obtained in the final exam to those previously obtained in the partial exam considered as passed (with a minimum grade of 3.5 points out of 10 points in each of the parts that compose it).

  On the day established by the Center for the ordinary exam, first of all, all students taking the exam will be examined on the contents corresponding to topics 5 and 6. Subsequently, those students who have not passed the partial exam or choose to retake the partial exam, waiving the grade obtained in the previous partial exam, will be examined on the contents corresponding to the first four topics.

  In those cases in which the student does not obtain a minimum grade of 3.5 points out of 10 points in each of the parts (theory and theoretical-practical), both in the exam corresponding to the first four topics and in the exam corresponding to topics 5 and 6, the overall grade of the knowledge acquired in the subject and, therefore, the grade that will appear in the corresponding report will be the sum of the scores obtained in the partial and final exam, with a maximum of 3 points. The student who does not appear for this final exam will have the qualification of "Not presented". The theoretical part will consist of a series of multiple-choice questions with a single correct answer. Wrong answers score negatively (the penalty will be notified to the student), unanswered questions do not add or subtract. The theoretical-practical will consist of solving exercises.

If student would take the partial exam again on the ordinary call, he/she will renounce to the grade obtained in the previous partial exam. In such a case, the grade obtained in this new exam will replace the previous one, if any.

In the extraordinary call, the assessment will be carried out entirely through an extraordinary exam, corresponding to the six topics, out of a total score of 10 points, even if during the development of the subject the continuous assessment system had been chosen.

As in the ordinary call, this exam will consist of two parts: theory and practice, which will be weighted at 30% and 70% respectively (theory 3 points and practice 7 points). To pass the subject, the student must obtain a minimum of 3.5 points out of 10 points in each of these parts (theory -1.05 points-and practice -2.45 points-). When this last requirement is not met, the overall exam grade and, therefore, the final grade of the subject will be the sum of the marks obtained with a maximum of 3 points. Likewise, the total score must be 5 points out of 10 to pass the subject. The student who does not take this final exam will have the grade of "Not presented".

The theoretical part will consist of a series of multiple-choice questions with a single correct answer. Wrong answers score negatively (the penalty will be notified to the student), unanswered questions do not add or subtract. The practice will consist of solving exercises.

Being an extraordinary call, the previous qualifications obtained in the continuous assessment system or final single assessment will not be considered.

In the single final assessment, the evaluation will be carried out entirely through an extraordinary exam, corresponding to the six topics, out of a total score of 10 points.

As in the ordinary call, this exam will consist of two parts: theory and practice, which will be weighted at 30% and 70% respectively (theory 3 points and practice 7 points). To pass the subject, the student must obtain a minimum of 3.5 points out of 10 points in each of these parts (theory -1.05 points-and practice -2.45 points-). When this last requirement is not met, the overall exam grade and, therefore, the final grade of the subject will be the sum of the marks obtained with a maximum of 3 points. Likewise, the total score must be 5 points out of 10 to pass the subject. The student who does not take this final exam will have the grade of "Not presented".

The theoretical part will consist of a series of multiple-choice questions with a single correct answer. Wrong answers score negatively (the penalty will be notified to the student), unanswered questions do not add or subtract. The practice will consist of solving exercises.

Students must necessarily be provided with the respective D.N.I., driver's license or official passport to take any of the programmed exams.