Numerical Techniques 1: Monte Carlo Simulation
Course Outline
Over the past two decades increased changes in the complexity of financial products and increasing computational capacity has meant that Monte Carlo methods have become the mainstay of any financial engineer's toolkit. This course illustrates how Monte Carlo can be used in modern finance for both pricing and risk management purposes. The course uses a combination of theoretical sessions with practical computer demonstrations and exercises to give delegates hands-on experience. Recent innovations are discussed including variance reduction techniques and quasi-random numbers to improve computational efficiency, using copulae for multi-variate problems, application of likelihood ratio methods to compute greeks, and methods for applying early exercise within a Monte Carlo framework. Theoretical concepts are demonstrated by practical applications to a range of different stochastic processes including both stochastic volatility and jumps. Techniques using Monte Carlo to sample extreme events are discussed with risk management applications to VaR and Counterparty risk.
Presented by Simon Acomb.
Who The Course is For
- Financial engineers
- Risk managers
- Model control and validation
- Quantitative traders
- IT professionals and system developers
- Financial control
- Front and middle office staff willing to extend their numerical skills
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Prior Knowledge
- Numerate background (familiar with differential calculus)
- Basic knowledge of derivative instruments
- Excel and basic VBA skills
This
program is eligible for
16 Continuing Education credit hours from the CFA Institute. If you are a
CFA Institute member, CE credit for your participation in this program
will be automatically recorded in your CE Diary.
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Day One
Introduction to the Monte Carlo Method
- Origins of the Monte Carlo method
- Foundations of probability and stochastic processes
- Fundamentals of applying Monte Carlo methods to finance
- Comparison with alternative numerical methods: trees and PDEs
- Practical issues in computer implementation: multi-threading, using an object orientation paradigm to ensure flexibility
Mathematics of Monte Carlo Simulations
- Generating random numbers
- Creating normal variates: Box-Muller vs inverse cumulative normal
- Path generation using the incremental method
- Multi-variate products and correlation
- Salvaging a good correlation matrix from bad data
- Generating multi-variate paths with Cholesky decomposition
- Continuous features and Monte Carlo
- Barriers and Lookbacks
Copulae and Local Volatility
- Building a local volatility Monte Carlo
-
Practicalities of building a local volatility surface:
- choosing a time step
- using higher order Monte Carlo methods
- Monte Carlo and implied probability distributions
- Using a Gaussian copula as an alternative to local volatility
- The problem of pricing basket options
- Pricing cliquets with copulae
- Using non-Gaussian copulae
Improving Efficiency
-
Variance reduction techniques:
- Antithetic sampling
- use of control variates
- importance sampling
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Quasi random numbers:
- features and properties of Sobol sequences
- using quasi-random numbers in high dimensions
- Alternative methods of path construction: Brownian bridges
Day Two
Calculating Greeks
- Difficulties in calculating greeks
- Recycling paths
- Speeding up calculations - where are the bottlenecks?
- Dealing with model consistency
- Using a likelihood ratio method
- Alternative ways of calculating greeks
Stochastic Volatility and Jump Models
- Introduction to Stochastic Volatility: Heston and the alternatives
- Discretisation methods : Euler and Milstein
- Sampling directly from the spot distribution
- Adding jumps: the Poisson process
- Issues in calibration
- Implementing hybrid models
- Stochastic volatility + jumps
- Stochastic volatility + local volatility
Early Exercise and Bermudean Options
- Formulating the problem of early exercise: comparing backwards and forward problems
- Using parametric exercise boundaries
- Practical implementation of simple methods
- Regression method of Langstaff and Schwartz
- Alternative methods for Early Exercise
Monte Carlo Applied to VaR and Counterparty Risk
- Simulating real distributions for VaR
- Calculating VaR using Monte Carlo and full revaluation
- Gaining efficiency in VaR calculations
- Sampling extreme events and looking in tails of distributions
- Counterparty risk as an extension of VaR
- Should Monte Carlo methods be used for counterparty risk?
