Simulation of Financial Scenarios | Postgraduate Program in Financial Management Engineering

Simulation of Financial Scenarios

Κωδικός Μαθήματος: 
I-8
Τύπος Μαθήματος: 
Υποχρεωτικό Μάθημα Κατεύθυνσης
Έτος Σπουδών: 
Α'
Εξάμηνο Σπουδών: 
Εαρινό
Αριθμός Πιστωτικών Μονάδων (ECTS): 
8
Γλώσσα Διδασκαλίας: 
Greek
Περιγραφή: 

Stochastic processes in finance: The need for simulation. A basic model for the evolution of stock prices: the random walk model. From random walk to Brownian motion & from Brownian motion to geometric Brownian motion. The Black-Scholes equation: Introduction to financial option valuation. Pricing of European options with the binomial tree. Pricing of European options with the trinomial tree. Monte Carlo simulation methods, part I: Application to financial option valuation under the riskneutral measure. Monte Carlo simulation methods, part II: variance reduction techniques. Monte Carlo simulation methods, part III: pricing of exotic options. Monte Carlo simulation methods, part IV: simulation of stochastic volatility models: Application in options pricing. Evaluation of a portfolio's risk with the value-at-risk method: Monte Carlo and empirical simulation techniques.

Προαπαιτήσεις: 

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Περιεχόμενο του μαθήματος (Syllabus): 

Every part of the syllabus is accompanied by laboratory applications using the R environment.

  1. Search for, analysis and synthesis of data and information, with the use of the necessary technology
  2. Adapting to new situations
  3. Decision-making
  4. Working independently
  5. Team work
  6. Working in an international environment
  7. Working in an interdisciplinary environment
  8. Production of new research ideas
  9. Criticism and self-criticism
  10. Production of free, creative and inductive thinking
Συνιστώμενη Βιβλιογραφία προς μελέτη: 
  • Brandimarte, P., Numerical Methods in Finance. A MATLAB Based Introduction, Wiley, 2002.
  • Glasserman, P., Monte Carlo Methods in Financial Engineering, Springer-Verlag, 2003.
  • Higham, D., An Introduction to Financial Option Valuation, Cambridge, 2005.
  • L. Clewlow, C. Strickland. Implementing Derivatives Models (1998). Wiley.
  • Hull, J., Options, Futures and other derivatives, Prentice Hall, 2014.
  • Neftci, S., Introduction to the Mathematics of financial derivatives, Academic Press, 2000
Διδακτικές και Μαθησιακές Μέθοδοι: 

Use of ICT in teaching and communication with students

Μέθοδοι αξιολόγησης / βαθμολόγησης: 

(Individual) Project based on the taught material that weights 100% on the calculation of the final grade.

Αντικειμενικοί Στόχοι μαθήματος (επιδιωκόμενα μαθησιακά αποτελέσματα): 

This course is an effort to address vital financial related problems based on both classical and modern algorithmic methods. The algorithmic techniques presented here find a wide range of applications in  every aspect of modern finance, with particular emphasis on the modeling of variability and uncertainty that characterizes financial markets. This course focuses on the standard algorithmic procedures that apply for the simulation of various financial scenarios. More specifically, the Monte Carlo family of simulation methods is applied to a wide range of financial related problems (with particular emphasis given on the valuation of various financial derivatives products (options; both vanilla and exotic), and portfolio risk quantification by using the Value at Risk method). Finally, alternative pricing methods (such as binomial trees, trinomial trees) are presented keeping in line with the classical model of Fisher Black and Myron Scholes. Upon the successful completion of the course, students will be able to:

  • simulate basic important stochastic processes that appear naturally in Finance (random walk, Brownian motion, Geometric Brownian motion), have a deep understanding of their statistical structure, and simulate a required number of paths for the above stochastic processes.
  • have a deep understanding of the main philosophy behind the tree methods for pricing options (binomial and trinomial tree).
  • write code for the pricing of European (and exotic) options with tree methods (binomial & trinomial).
  • have understood the limiting relationship between the binomial option pricing model and the Black-Scholes model and also to be able to write code (in R) that implements the Black-Scholes pricing model.
  • apply Monte-Carlo simulation methods to a wide range of financial problems with emphasis in option valuation (European and mainly Exotic options).
  • know the basic variance reduction techniques for the Monte-Carlo method (antithetic variates, control variates).
  • know how to simulate the basic stochastic processes that describe the evolution of the volatility of stock prices (stochastic variability models; Heston model, Hull-White model).
  • apply Monte Carlo option pricing techniques under stochastic volatility models.
  • access the risk of a portfolio (value-at-risk method).
Περίγραμμα του Μαθήματος: 
PDF icon 3.SIMULATION OF FINANCIAL SCENARIOS.pdf