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Course module: 35V5A1-B-6
35V5A1-B-6
Quantitative Finance
Course info
Course module35V5A1-B-6
Credits (ECTS)6
CategoryBA (Bachelor)
Course typeCourse
Language of instructionEnglish
Offered byTilburg University; Tilburg School of Economics and Management; TiSEM: Econometrics and OR; Econometrics & Operations;
Is part of
B Econometrics and Operations Research
Lecturer(s)
Lecturer
dr. R. van den Akker
Other course modules lecturer
Lecturer
J.T.G. Goossens, MSc
Other course modules lecturer
Lecturer
prof. dr. B.J.M. Werker
Other course modules lecturer
Academic year2020
Starting block
SM 1
Course mode
Full-time
RemarksCaution: this information is subject to change
Registration openfrom 25/08/2020 up to and including 20/08/2021
Aims

The course Quantitative Finance provides an introduction to financial engineering. Financial engineering is a multidisciplinary field that uses techniques and theories from (mathematical) finance, computational finance, operations research, probability theory, statistics & data science, and economics. Practitioners working on financial engineering problems are often called “quants”. Quants typically work at banks, insurance companies and pension funds, and at traders.

Important topics in Financial Engineering include:

  • The modelling of asset prices (how will the price of, for example, a commodity as gold, or the stock Royal Dutch Shell evolve over time)?
  • The valuation of financial derivatives (contracts whose cashflows are related to the price evolution of other financial assets).
  • Measurement of risk (in, for example, a trading portfolio or a balance sheet).
  • The use of financial instruments to reduce (hedge) risk.
  • Optimal allocation of assets.

The course Quantitative Finance will provide you with the mathematical tools (continuous-time stochastic processes, martingales, stochastic integrals and differential equations, and Itô calculus) in order to be able to formulate continuous-time models for asset prices. Using the no free lunch principle and replication portfolios, you will learn two methods for the valuation of financial derivatives: the Partial Differential Equation method and the method of “risk-neutral pricing” also known as the “equivalent martingale measure approach”. In particular cases it is possible to obtain “closed-form formulas” for the solution to a stochastic differential equation (SDE) or the price of a financial derivative. An important example is the famous Black-Scholes formula, for which Robert C. Merton and Myron Scholes received the 1997 Nobel Memorial Prize in Economic Sciences. As it is not always possible to derive closed-form formulas, we will also discuss numerical techniques, most prominently Monte Carlo methods, in order to obtain numerical approximations.

Content
Learning goals
  • Students are able to formulate the main results of Itô calculus, provide proofs of these results, and to apply this calculus.
  • Students are able to develop continuous-time models for the evolution of equity prices; are able to derive the value and hedge for financial derivatives (given a continuous-time model for the underlying asset).
  • Students can simulate financial models with Monte Carlo methods and know how to make these simulations more efficient through variance reduction and importance sampling.
Examination
Written exam (80%), and two assignments (10% each). The assignments can be done in groups (max. 3 students).

Type of instructions
Lectures, tutorials 

Compulsory Reading
Slides and lecture notes.

Recommended Reading
  • Baxter, M. and A. Rennie (1996). Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press.
  • Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York.
  • Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition, 9/E, Pearson.
  • Mikosch T. (1998). Elementary Stochastic Calculus, With Finance In View, World Scientific Publishing Co Pte Ltd.

Recommended Prerequisites

Linear Algebra, Probability and Statistics, Introduction Finance & Actuarial Science, Differentiation and Integration Theory, Introduction Asset Pricing, Mathematical Analysis 2, Statistics for Econometrics, basic programming skills
Course available for exchange students
Conditions of admission apply
Contact person
dr. R. van den Akker
Timetable information
Quantitative Finance
Written test opportunities
DescriptionTestBlockOpportunityDate
Written test opportunities (HIST)
DescriptionTestBlockOpportunityDate
Written exam (80%) / Written exam (80%)EXAM_01SM 1115-12-2020
Written exam (80%) / Written exam (80%)EXAM_01SM 1218-01-2021
Required materials
-
Recommended materials
-
Tests
Assignment (20%)

Written exam (80%)

Final grade

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