Derivative Pricing

Advanced courses in probability theory and finance course covering financial markets and products. Corresponding UCl course:

• LLSMS2225 (Elements of Stochastic calculus)
• LLSMS2100 (Advanced Finance)

1. Part I : Black-Scholes Model (discrete time Cox-Ross-Rubinstein, continuous time model Black-Scholes-Merton, greeks)
2. Part II: arbitrage-free pricing (fundamental theorem of asset pricing).
3. Part III : Interest rates products (FRAs, Swaps, caps, floors) and pricing (affine short rate model, arbres binomiaux).
4. Part IV : Limits of the model and advanced methods.

At the end of this course, the student will able to : 

• To describe the use and the mechanics of derivatives in general, and in particular discuss their advantages and disadvantages for the society as a whole.
• Explain the principles of arbitrage-free valuation, and to interpret the price of such derivatives as the cost of setting up a self-financing replication strategy.
• Apply pricing strategies to value certain productsby using either analytical or numerical methods
• Discuss the use and misuse of pricing models

LSM competency framework : 2.2, 2.3, 2.4, 3.1, 6.1, 8.1, 8.3

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.

An oral exam (60%) made of two parts:

1. practice and theory.
2. Two team works (25%) and one individual work (15%) that will be discussed at the exam.

• 15 courses of 2 hours including exercices and programming sessions.
• Team works on R and Bloomberg.The students will also be invited to introduce themselves some financial products and discuss some methods to valkue and hegde those

The objective of this course is to introduce fundamental concepts valuing derivatives using the no-arbitrage assumption.

• Slides, Excel workbook and R code.

• Lectures conseillées :

  - Hull, J. Options, Futures and Other derivatives.

  - Portrait & Poncet, Finance de marché, Dalloz, 2009.

  - Joshi, M. : Concepts and Practice of Mathematical Finance, Cambridge University Press, 2003.

  - Shreve, S. : Stochastic calculus for Finance I & II, Springer 2004.