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401-4922-08L 4 Credits DR , MSC D-USYS , D-MTEC , D-BAUG , D-MAVT , D-INFK , D-MATH , D-BIOL , D-ERDW , D-GESS , D-ITET , D-CHAB

Monte-Carlo Methods for Finance and Insurance

Lecturers: Prof. em. Dr. Paul Embrechts, Prof. Dr. Don McLeish
Examiners: Prof. em. Dr. Paul Embrechts
VVZ CR n/a

Last Updated: 2026-02-05 15:29:50

Abstract

This course treats the following topics:(1) Basic Monte Carlo simulation: generating pseudo-random numbers from a variety of distributions.(2) Variance reduction techniques.(3) Statistical Methods and Simulation.(4) Simulation of Continuous-Time Models.Examples will mainly come from the realm of finance and insurance.

Objective

This course treats a selection of the following topics: (1) Basic Monte Carlo simulation: generating pseudo-random numbers from a variety of distributions. Monte-Carlo option pricing and Risk Measures. (2) Variance reduction techniques: •Antithetic Random numbers (call option pricing) • Control Variates (call option pricing) • Conditioning (Heston Example) • Stratified Sampling • Importance Sampling; rare event simulation, pricing CDOs • Combining estimators • Low Discrepancy Sequences and Quasi Monte Carlo (3) Statistical Methods and Simulation • The statistical bootstrap (Efron and Tibshirani, 1993) • Markov Chains and MCMC, Gibbs sampling. • Missing and incomplete data. (4) Simulation of Continuous-Time Models • Crude simulation of an option price in continuous‐time model. Euler and Milstein methods. • Estimating and simulating volatility. • Simulating Barrier/lookback options, survivorship bias • Continuous‐time Stochastic Volatility models: Pricing options by simulation • Asset Allocation and Portfolio Selection under Stochastic parameters • Simulating a Ruin Process

Content

This course treats a selection of the following topics: (1) Basic Monte Carlo simulation: generating pseudo-random numbers from a variety of distributions. Monte-Carlo option pricing and Risk Measures. (2) Variance reduction techniques: •Antithetic Random numbers (call option pricing) • Control Variates (call option pricing) • Conditioning (Heston Example) • Stratified Sampling • Importance Sampling; rare event simulation, pricing CDOs • Combining estimators • Low Discrepancy Sequences and Quasi Monte Carlo (3) Statistical Methods and Simulation • The statistical bootstrap (Efron and Tibshirani, 1993) • Markov Chains and MCMC, Gibbs sampling. • Missing and incomplete data. (4) Simulation of Continuous-Time Models • Crude simulation of an option price in continuous‐time model. Euler and Milstein methods. • Estimating and simulating volatility. • Simulating Barrier/lookback options, survivorship bias • Continuous‐time Stochastic Volatility models: Pricing options by simulation • Asset Allocation and Portfolio Selection under Stochastic parameters • Simulating a Ruin Process

Resources

Lecture Notes

The course is based on the following text:Don L. McLeish (2005) Monte-Carlo Simulation and Finance. Wiley, New York.Students will get access to course slides.

Literature

Don L. McLeish (2005) Monte-Carlo Simulation and Finance. Wiley, New York.

General Information

Language
English
Levels
DR , MSC

Examination

Type
session examination
Mode
written 120 minutes
Aids
None

Course Components

Type Title Time & Place Hours
lecture Monte-Carlo Methods for Finance and Insurance
  • Thu 15:15-17:00 (ML F 39)
2 h weekly

Offered In