CFRM 548: Monte Carlo Methods in Finance

This course covers a broad range of standard and specialized Monte Carlo methods in finance with a focus on accurate derivative pricing. Students will learn the theoretical rationale for the methods and will gain applications knowledge through programming assignments using R or Matlab. The course will begin with an overview Monte Carlo methods and a review of basic derivative pricing method. Topics covered will include:

  • Derivative pricing methods: replication, no-arbitrage, risk-neutral pricing, change of numeraire
  • Random number generators: linear congruential generators, lattice structure, simulation error
  • Sampling methods: inverse transform, acceptance-rejection methods
  • Mulivariate random numbers: normal distributions, t-distributions, stable distributions
  • Simulating sample paths: univariate and multivariate GBM, path-dependent options, short-rate models and bond prices
  • Simulating advanced models: square-root diffusions and bond prices, forward rate models and pricing derivatives, jump processes
  • Variance reduction methods: antithetic variables, control variates, stratified sampling, Latin hypercube sampling, matching methods, importance sampling
  • Discretization methods: Euler method, second-order methods, applications to extremes and barrier crossings
  • Estimating the Greeks sensitivity measures: finite-difference approximations, pathwise derivative estimates, likelihood ratio method
  • Pricing American options: random tree methods, stochastic mesh methods, regression methods
  • Risk management applications: calculating VaR and CVaR, calculating VaR and CVaR portfolio risk decompositions, delta-gamma based variance reduction, methods for fat-tailed distributions
Steve Golbeck
Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering, Springer
R and R Finance Packages or Matlab
CFRM 544 or equivalent, or by permission.