INSTITUTE OF APPLIED MATHEMATICS
Last Updated:
28/08/2017 - 21:10

IAM757 - Special Topics: Monte Carlo Methods in Finance and Insurance

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Ömür Uğur
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Generating Random Numbers; Basic Principles of Monte Carlo; Numerical Schemes for Stochastic Differential Equations; Simulating Financial Models; Jump-Diffusion and Levy Type Models; Simulating Actuarial Models; Markov Chain Monte Carlo Methods.

Course Objectives

At the end of this course, the student will learn:

  • the generation of pseudorandom numbers from a given distribution
  • basics of Monte Carlo methods and variance reduction techniques
  • the algorithms for numerical solutions of stochastic differential equations, such as Euler-Maruyama and Milstein schemes, and convergence of numerical methods
  • the simulation of Levy processes, in particular, jump-diffusion processes by Euler-Maruyama method for jump-diffusions
  • possible fields of applications of continuous-time stochastic processes with continuous and discontinuous paths
  • basic principles of Markov chain Monte Carlo methods and Bayesian estimation

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

  • generate pseudorandom numbers from a given distribution that is commonly used in finance and/or insurance
  • apply Monte Carlo methods and variance reduction techniques to approximately integrate, or take, the underlying expectation and moments of random variables
  • simulate continuous-time stochastic processes with continuous and discontinuous paths; characterise the convergence and rate of convergence of the numerical schemes used
  • apply the methods to models in finance and/or insurance, such as pricing models under Black-Scholes or Heston model settings, interest rate models as well as derivatives, risk measures, pricing longevity products
  • learn basics of Markov chain Monte Carlo methods and Bayesian estimation in actuarial mathematics

Tentative (Weekly) Outline

  1. Generating Random Numbers
  2. Generating Random Samples (Numbers) from a Specified Distribution
  3. Monte Carlo Method and Integration
  4. Variance Reduction Techniques: Antithetic and Control Variates
  5. Variance Reduction Techniques: Stratified, Conditional, and Importance Sampling
  6. Some Applications from Finance and Insurance
  7. Numerical Schemes for Stochastic Differential Equations: Euler-Maruyama
  8. Numerical Schemes for Stochastic Differential Equations: Milstein scheme and Lamperti transform
  9. Convergence Analysis of Numerical Schemes and Extrapolation Methods
  10. Basics of Multilevel Monte Carlo Method
  11. Numerical Solutions of Jump-Diffusion Processes
  12. Simulation of Lévy Processes
  13. Some Applications from Finance and Insurance
  14. Basics of Markov Chain Monte Carlo and its Applications

Course Textbook(s)

  • R. Korn, E. Korn, G. Kroisandt, Monte Carlo Methods and Models in Finance and Insurance, Chapman & Hall/CRC, 2010

Supplementary Materials and Resources

Books
  • P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2003
  • G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications, Springer, 1996
Readings
  • Some of the papers or resources on the wikipage (https://en.wikipedia.org/wiki/Monte_Carlo_method) and the references therein might be useful and interesting to read and work on.

More Info on METU Catalogue

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