core processes
Download
Skip this Video
Download Presentation
Core Processes

Loading in 2 Seconds...

play fullscreen
1 / 15

Core Processes - PowerPoint PPT Presentation


  • 147 Views
  • Uploaded on

Core Processes. PDE theory in general Applications to financial engineering State of the art finite difference theory Applying FDM to financial engineering Algorithms and mapping to code. PDE Theory. Continuous problem classification Concentrate on 2 nd order parabolic equations

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Core Processes' - ata


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
core processes
Core Processes
  • PDE theory in general
  • Applications to financial engineering
  • State of the art finite difference theory
  • Applying FDM to financial engineering
  • Algorithms and mapping to code
pde theory
PDE Theory
  • Continuous problem classification
  • Concentrate on 2nd order parabolic equations
  • In fact, convection-diffusion equations
  • Existence, uniqueness and other qualitative properties
pde and financial engineering
PDE and Financial Engineering
  • Derive PDE from Ito’s lemma
  • Applicable to a range of plain and exotic option problems
  • Document and standardise option classes
  • Concentrate on one-factor and two-factor models
examples
Examples
  • Standard Black Scholes PDE (different underlyings)
  • Barrier options
  • Asian options
  • Other path-dependent options
  • Several underlyings
other pde types
Other PDE Types
  • First-order hyperbolic equations
  • ‘Mixed’ (e.g. parabolic/hyperbolic)
  • Systems of equations
  • Parabolic Integral Differential Equations (PIDE)
  • Free and moving boundary value problems
finite difference methods
Finite Difference Methods
  • Lots of choices!
  • Choosing the most appropriate one demands insight and experience
  • Using a numerical recipe approach does not always work well 
  • This course resolves some of the problems and misunderstandings
fdm types 1 2
FDM Types (1/2)
  • Standard recipes (e.g. Crank Nicolson)
  • Special FDM for difficult problems
  • FDM for multi-dimensional problems
  • FDM and parabolic variational inequalities
standard fdm
Standard FDM
  • Crank Nicolson
  • The standard FDM for many problems
  • Does not work well in all cases
  • This course tells why (and how to resolve the problem)
special fdm
Special FDM
  • Needed when we wish to address some difficult issues
  • Standard recipes need to be replaced in thee cases
  • We must defend why we need thee new schemes
what are the problems
What are the Problems?
  • Producing stable and oscillation-free schemes
  • Approximating the Greeks
  • How to solve multi-dimensional problems
  • Modeling free boundaries and the American exercise variation
special schemes 1 2
Special Schemes (1/2)
  • Fitted schemes
  • Oscillation-free scheme
  • The Box scheme (modelling Black Scholes as a first-order systems)
  • Van Leer and other nonlinear schemes
special schemes 2 2
Special Schemes (2/2)
  • Schemes for multidimensional problems
  • ‘Direct’ schemes
  • ADI (Alternating Direction Implicit)
  • Splitting methods (Janenko)
supporting techniques 1 3
Supporting Techniques (1/3)
  • Fourier series/transforms
  • Ordinary Differential Equations (ODE)
  • Stochastic Differential Equations (SDE)
  • Theory of PDE
supporting techniques 2 3
Supporting Techniques (2/3)
  • Finite differences for ODE and SDE
  • Method Of Lines (MOL) and semi-discretisation
  • Spectral and pseudospectral methods
  • (Finite Element/Volume methods)
supporting techniques 3 3
Supporting Techniques (3/3)
  • Numerical differentiation, integration and interpolation
  • Matrix algebra; solution of linear equations
  • Discrete methods for PVI
  • Monte Carlo, binomial and trinomial methods
ad