FIN-404 / 6 crédits

Enseignant: Hugonnier Julien

Langue: Anglais

## Summary

The objective of this course is to provide a detailed coverage of the standard models for the valuation and hedging of derivatives products such as European options, American options, forward contracts, futures contract and exotic options.

## Keywords

Derivatives, options, arbitrage valuation, hedging

## Required courses

• Introduction to finance
• Stochastic calculus

• Econometrics

## Important concepts to start the course

To follow this course students need to have taken an introduction to finance, and must possess solid foundations in probability theory and stochastic calculus.

## Learning Outcomes

By the end of the course, the student must be able to:

• Describe the principal types of derivatives contracts including forwards, futures and options and compare their basic usages for hedging or speculation
• Describe and analyse the most common types of options strategies such as spreads, straddles, collars, and covered calls or puts.
• Formulate the no-arbitrage principle and illustrate its basic application in a model-free setting: cash and carry relations for different types of underlying securities with or without dividends, put/call parity, arbitrage bounds on option prices, early exercise of American options.
• Discuss the main characteristics of a general discrete time model with finitely many states of nature, multiple securities and possibly stochastic interest rates.
• Work out / Determine whether a given discrete-time model with finitely many states of nature is arbitrage free and has complete markets; Relate these properties to the existence and uniqueness of an equivalent martingale measure.
• Discuss and apply risk-neutral valuation to price and hedge derivatives of either European or American type in the context of a given discrete time model with finitely many states and complete markets.
• Construct and implement a binomial model to price and hedge both plain vanilla derivatives of European or American type as well as any exotic derivative.
• Describe the main assumptions of the Black-Scholes model and its limitations, derive the valuation partial differential equation and the Black-Scholes-Merton formula for the price of standard European options.
• Discuss the main option Greeks and use them appropriately for risk management and financial engineering purposes in the context of the Black-Scholes model or its extensions to futures contracts and foreign exchange.
• Work out / Determine whether a general Brownian-driven model of financial markets admits an equivalent martingale measure, relate the uniqueness of this probability measure to market completeness, and derive the risk-neutral dynamics of traded securities prices and relevant state variables.
• Derive the partial differential equation satisfied by the price of a European derivative in a given Markovian model, and use it with appropriate boundary conditions to price options in specific models.
• Formulate the valuation of American options as a free boundary problem for the valuation PDE in the context of the Black-Scholes model, derive and discuss exact solutions for the infinite horizon case and the Barone-Addesi-Whaley approximation for the finite horizon case.

## Transversal skills

• Plan and carry out activities in a way which makes optimal use of available time and other resources.
• Evaluate one's own performance in the team, receive and respond appropriately to feedback.
• Continue to work through difficulties or initial failure to find optimal solutions.
• Use both general and domain specific IT resources and tools

## Teaching methods

Lectures and exercise sessions

## Expected student activities

• Participate in weekly lectures
• Participate in weekly exercise sessions
• Turn in assignements/projects
• Write a midterm exam (30%) and a final exam (40%)

## Assessment methods

• Assignment/Project: 30%
• Midterm exam: 30%
• Final exam: 40%

## Bibliography

• K. Back, A course in derivative securities, Springer Verlag, New York, 2005.
• N. Bingham and R. Kiesel, Risk neutral valuation, Springer Verlag, New York, 2004.
• J. Hull, Options, futures and other derivatives, Prentice Hall.
• D. Lamberton & B. Lapeyre, Introduction to stochastic calculus applied to finance, Second edition, Chapman and Hall, 2008.
• S. Shreve, Stochastic Calculus for Finance I and II, Springer Verlag, New York, 2004.
• T. Bjork, Arbitrage theopry in continuous-time, 2nd Edition, Oxford University Press, New York, 2004

## Prerequisite for

• Financial econometrics (taken concurrently)
• Interest rate and Credit risk models
• Quantiative Risk Management
• Real options and financial structuring

## Dans les plans d'études

• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Derivatives
• Cours: 3 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Derivatives
• Cours: 3 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Derivatives
• Cours: 3 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Derivatives
• Cours: 3 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Printemps
• Forme de l'examen: Ecrit (session d'été)
• Matière examinée: Derivatives
• Cours: 3 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 ELA2 10-11 BS170 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

Mardi, 9h - 12h: Cours ELA2

Jeudi, 10h - 12h: Exercice, TP BS170

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