Course: 2024/2025

(16755)

Requirements (Subjects that are assumed to be known)

Introduction to the Financial Markets
Programación de Altas prestaciones.
Sistemas de Información.

Familiarize yourself with the roles and profiles in the financial markets area.
Understand the main challenges in the field of quantitative finance and risk management in financial markets.
Ability to assimilate the mathematical, technological, and financial fundamentals involved in the valuation of derivative products.
Know and assimilate the specific programming knowledge related to the valuation and risk management of derivative products.
Understand the computational challenges related to the design of financial software, especially those related to the calculation of sensitivities of derivative products.
Students should be able to apply the knowledge acquired and their problem-solving abilities in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.
Students should have the learning skills that enable them to continue studying in a largely self-directed or autonomous manner.
Ability to understand and apply methods and techniques from the field of Computer Engineering in financial markets.
Ability to conceive, design, create, implement, and adopt a substantial development or creation process for financial market software.
Ability to apply the knowledge acquired and solve problems in new or unfamiliar environments within broader and multidisciplinary contexts, integrating this knowledge.
Ability to work in multidisciplinary environments and in large, heterogeneous development teams.
Participate in the development of financial software, from its conception in the analysis phases to its implementation and integration with other systems.
Implement classic algorithms and techniques in financial markets following the established standards and procedures at all times.
Learning outcomes:
Know the main programming languages used for financial software development.
Ability to implement software for the financial sector.
Knowledge of high-performance programming.
Know the main algorithms used in the financial sector, both in the front office and the back office.
Ability to implement classic financial algorithms across all layers.
Know the main available Open Source initiatives.
Understand the life cycle of financial applications.
Ability to validate and verify financial software.
Know the main management tools.
Understand Project Management in Financial Environments

Skills and learning outcomes

Description of contents: programme

SIMPLIFIED PROGRAM
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1. Introduction to Financial Calculus
2. Algorithms for Calculating Returns
3. Calculation of Provisions and Reserves
4. Open Source Financial Platforms and Tools
5. Development of Practices and Labs
DETAILED PROGRAM
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0. Introduction to Back-Office Algorithms
- Jupyter Notebooks in C++
1. Introduction to Financial Markets:
- Basic Concepts in Finance
- Classification of Financial Markets
- Key Roles in Financial Markets
- Career Paths in Financial Markets.
2. Interest Rates, Bonds, and Interest Rate Derivatives
- Introduction
- Bonds
- Interest Rate Derivatives
- Markets
- Discount Factors
- Certificate of Deposit and Libor Rates
- FRAs
- Futures
- Interest Rate Swaps
- Multi-currency Instruments
- Multi-currency Valuation
- Forex Swaps
- Cross-Currency Basis Swaps
3. Construction of Interest Rate Curves and Risk Management for Linear Products (IR Delta)
- Introduction
- Practical Terms of Interest Rate Curve Construction
- Interpolation Methods
- Interpolators
- Detailed Construction of Interest Rate Curves
- Instrument Curves: Residual Calculation
- Risk Management of Linear Products: IR Delta Management
- Par-Point Calculation
- Accumulated Increments
- Analytical Sensitivities: Case of Interest Rate Swap
4. Risk Metrics: P&L Analysis and Value-at-Risk
- P&L Analysis
- Calculation of Risk Metrics
- P&L Analysis Techniques
- P&L Prediction
- P&L Explanation
- Value-at-Risk and Expected Shortfall
- Use of VaR Metrics
- VaR with Historical Data
- Model VaR: Linear Model
5. Options. The Black-Scholes-Merton Model
- Brownian Motion
- Itô's Lemma
- Delta Hedging
- Basic Concepts of Options
- The Black-Scholes-Merton Model
- Black-Scholes-Merton SDE
- The Black-Scholes-Merton Formula
- The Black76 Formula
- Deriving the Black-Scholes-Merton Formula
- Greeks
- Delta
- Gamma
- Theta
- Relationship between Delta, Theta, and Gamma
- Vega
- Rho

Learning activities and methodology

AF1: Theory classes: Basic theoretical knowledge and skills will be presented in large groups. Attendance: 100%
AF3: Theory - practice classes: Theory lessons and resolution of practical exercises. Attendance: 100%
AF4: Laboratory sessions: Small groups classes, in which problems proposed to the students are discussed and developed using the computer. Attendance: 100%
AF5: Tutorials: Tutorials in person (one-by-one) or videoconference. Attendance: 100%
AF2: Learning activities: forum about subjects, recorded-contents and other educational activities. Attendance: 0%
AF7: Individual work. Attendance: 0%
Teaching methodologies:
MD1: Theoretical lectures to develop the main concepts of the subject
MD3: Practical cases and problems that students must solve individually or in small groups
MD4: Oral presentations and discussions in class under teacher moderation
MD5: Practical work individually or in small gropus
MD6: e-Learning activities
TUTORING REGIME
Individualized tutoring sessions can be requested and will be conducted virtually.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment

Basic Bibliography

- Hull, J.C.. Options, futures, and other derivatives.. Pearson. 2022

Additional Bibliography

- Joshi, M. The Concepts and Practice of Mathematical Finance. Cambridge University Press: Cambridge. 2003
- Marsden, J.E., Tromba, A.J. . Vector Calculus, W.H.. Freeman & Co Ltd: New York. 2013
- Neftci, S.N, . An Introduction to the Mathematics of Financial Derivatives. Academic Press: New York and Reading. 2000
- Piterbarg, V.V. and Andersen, L.B.G. Interest Rate Modeling. Atlantic Financial Press: London and New York. 2010
- Shreve, S. Stochastic Calculus for Finance II, Continuous-Time Models, Springer: Pittsburgh. Springer: Pittsburgh. 2004
- Spivak, M.. Calculus. Cambridge University Press: Cambridge. 1994
- Stroustrup B.. The C++ programming language . Addison Wesley. 2013
- Wilmott P., Howison, S. and Dewynne, J.. The Mathematics of Financial Derivatives. Cambridge University Press: Cambridge. 1995

The course syllabus may change due academic events or other reasons.