Course 2020-2021 a.y.


Department of Finance

Course taught in English
Go to class group/s: 31
DES-ESS (6 credits - II sem. - OP  |  SECS-P/01)
Course Director:

Classes: 31 (II sem.)

Suggested background knowledge

Students are recommended to have intermediate-level exposure to calculus (series and progressions, derivatives, Taylor polynomials, chain rule, implicit functions, unconstrained and constrained optimization), linear algebra (systems of linear equations, matrix algebra), statistics (multiple random variables, moments, hypothesis testing, linear regression models) and basic knowledge of Excel. Prior exposure to finance is beneficial, although not essential.

Mission & Content Summary


The course aims at providing the tools to examine economic activity in financial markets: how securities are priced and how are used. The course covers the essentials, while leaving more specialized topics to follow-up optional modules. Students gain a general knowledge of the valuation and use of bonds, stocks and derivatives within typical portfolio problems.


  • Deterministic cash flows. The basic premise in cash flow modeling is the understanding of the time value of money. Thus, the timing of cash flows affects asset values and rates of return. The simplest cash flows are those that are deterministic, either with one or several periods. Fixed-income securities belong to this class and can be analysed by means of interest rates.
  • Random cash flows. Typically, the initial cost of an investment is known, while its future cash flows are random. Cash flow uncertainty can be analysed by means of different techniques and we focus here on the mean-variance and the arbitrage analysis. The starting point of our analysis is that investors like returns and dislike risk. After defining precisely what the term risk means, we relate it to investments and look at methods to measure risk. Finally, we discuss the relation between risk and return, and use it to determine security prices.
  • Derivative cash flows. The next level of complexity pertains to cash flow streams that are random and depend functionally on another asset. We introduce simple derivative securities such as futures, forwards and (European) options and describe how they work. Pricing is done through arbitrage analysis and we see how derivative assets can be used to increase returns or limit losses.

Intended Learning Outcomes (ILO)


At the end of the course student will be able to...
  • Identify the quantitative models and methods for pricing financial assets.
  • Identify the quantitative models and methods for portfolio formation, i.e. bundling financial assets, in order to mitigate risk.


At the end of the course student will be able to...
  • Design a portfolio of bonds that minimizes interest rate risk (immunization).
  • Design a portfolio of stocks that is optimal in the mean-variance sense.
  • Design a portfolio of options that allows to profit from future movements in the underlying asset's price.

Teaching methods

  • Face-to-face lectures
  • Exercises (exercises, database, software etc.)


"Exercises" include:

  • Problem sets: at the end of each unit, exercises (problem sets) are circulated in class. Problem sets resemble the structure of the final exam, and thus serve as mock training. Problem sets do not count towards the course grade, but help in timely checking their knowledge acquisition as the course progresses.
  • Applications: at the end of each unit, we use laptops to implement some of the tools developed during the lectures with real world data.

Assessment methods

  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)


Written exam (Respondus Lockdown Browser and Monitor with embedded scientific calculator) consists of closed-ended questions aimed to assess students' ability to apply quantitative methods to the pricing of financial assets and to portfolio formation for both hedging/risk mitigation (e.g. bond portfolio immunization, mean-variance optimization) and speculation (e.g. directional and non-directional derivatives strategies) purposes. Detailed format: closed books, 12 questions, 60 minutes.  

Teaching materials


  • D.G. LUENBERGER, Investment Science, Oxford University Press, 2013, 2nd edition. The first edition (1998) would also work as well.
  • Lecture slides, academic papers and policy reports uploaded on Blackboard as the course progresses.
Last change 13/12/2020 18:34