MATH-470 / 5 credits

Teacher: Schmutz Michael

Language: English

## Summary

The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mathematics. Moreover, the concepts of complete and incomplete markets are discussed.

## Keywords

martingales, financial mathematics, theory of (no-)arbitrage

## Recommended courses

Stochastic calculation

## Important concepts to start the course

Stochastic calculation

## Learning Outcomes

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

• Explore in detail the use of martingales in financial mathematics.
• Prove a criteria for absence of arbitrage in a model based on a finite probability space and state an analogous general result.
• Prove a criteria for completeness of a market model based on a finite probability space and state an analogous general result.
• Explain the difference and the resulting consequences between claims and American options.
• Derive prices for some financial derivatives based on several different models.
• Derive different hedging strategies for some financial derivatives based on several different models.
• Analyze the choice of asset price models according to different criteria.
• Optimize the calibration of chosen asset price models.
• Prove a criteria for completeness of a viable market modeled based on a finite probability space and state an analogous general result.

## Assessment methods

Exam oral

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

## Supervision

 Office hours Yes Assistants No Forum No Others

## Bibliography

• Lamberton, D. and Lapeyre, B. (2008), Introduction to Stochastic Calculus Applied to Finance, Second Edition, Chapman and Hall, London.
• Shiryaev, A.N. (1999), Essentials of Stochastic Finance: Facts, Models, Theory, World Scientific Publishing, Singapore.
• Barndorff-Nielsen, O.E. and Shiryaev, A.N. (2015), Change of Time and Change of Measure, Second Edition, World Scientific Publishing, Singapore.
• Eberlein, E. and Kallsen, J. (2019), Mathematical Finance, Springer Finance, Cham.
• Jarrow, R.A. (2021), Continuous-Time Asset Pricing Theory, Second Edition, Springer Finance, Cham.

## In the programs

• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Martingales in financial mathematics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Martingales in financial mathematics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Martingales in financial mathematics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Martingales in financial mathematics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional
• Semester: Spring
• Exam form: Oral (summer session)
• Subject examined: Martingales in financial mathematics
• Lecture: 2 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: optional

## Reference week

 Mo Tu We Th Fr 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

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