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Continuous Time Finance (FIM)

MA9973Core area6 ECTSEnglishsummer semesterDepartment Mathematics
AI-edited module sheet. Based on the TUMonline module description, edited for readability.Original in TUMonline

What it is about

You will learn the mathematical foundations of financial models in continuous time: Ito calculus, stochastic processes as well as valuation and hedging of derivatives. In the end you will be able to apply the Black-Scholes model, assess arbitrage/completeness and implement numerical methods for simulation and pricing.

What you will be able to do

  • Apply the basics of Ito calculus
  • Utilize Girsanov, Lévy and Radon-Nikodym theorems
  • Understand no-arbitrage, completeness and risk-neutral valuation
  • Valuation and hedging of European options (Black-Scholes and generalizations)
  • Knowledge of extended models (stochastic volatility, jump models) and their advantages/disadvantages
  • Understand and implement numerical methods (Monte Carlo, Fourier-Pricing)

What the module consists of

  • LectureConveying theoretical foundations and proofs
  • Exercises / TutorialsSolving and discussion of exercise problems
  • Computer-based programming exercisesImplementation of numerical methods in Matlab or R

Teaching method

  • Lecture with slides and board proofsto explain theory and derive mathematical results
  • Problem sets and tutorialsfor practice and discussion of solutions
  • Instructor-supported programming tutorialsfor practically implementing numerical procedures
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Official page in TUMonline · Details are not binding.