MATLAB

• Available on computers in IEOR Computer Lab, 301 Mudd

  an online tutorial

Numerical Transform Inversion

There is an Extra-Credit Project on this. The specific assignment is an extra-credit numerical homework

Papers on inversion

All that should be necessary is a few pages from the first reference below. Do not be freaked out. I cite more to point you to where you might go next.

• Joseph Abate and Ward Whitt, Numerical Inversion of Laplace Transforms of Probability Distributions. ORSA Journal on Computing, vol. 7, 1995, pp. 36-43. [PDF] (See especially the Euler algorithm summarized on page 41.)

• Joseph Abate, Gagan L. Choudhury and Ward Whitt, An Introduction to Numerical Transform Inversion and its Application to Probability Models, in Computational Probability, W. Grassman (ed.), Kluwer, Boston, 1999, pp. 257-323 (with ). [PDF] (See especially the first 16 pages, with the short algorithm summary on page 16.)

• Joseph Abate and Ward Whitt, Numerical Inversion of Probability Generating Functions. Operations Research Letters, vol. 12, No. 4, 1992, pp. 245-251. [PDF]

• Gagan L. Choudhury, David M. Lucantoni and Ward Whitt, Multi-Dimensional Transform Inversion with Applications to the Transient M/G/1 Queue. Annals of Applied Probability, vol. 4, 1994, pp. 719-740 [PDF]

• For more related material, see my papers with Joe Abate and my papers with Gagan Choudhury

Applications of numerical inversion in finance

• Dmitry Davydov and Vadim Linetsky, Structuring, Pricing and Hedging Double-Barrier Step Options. Journal of Computational Finance, vol. 5, 2001-2, pp.55-87. [PDF from Linetsky's web page]

• Gianluca Fusai and Aldo Tagliani, Pricing of Occupation Time Derivatives: Continuous and Discrete Monitoring. Journal of Computational Finance, vol. 5, Fall 2001. [PDF from journal]

• Giovanni Petrella and Steven G. Kou, Numerical Pricing of Discrete Barrier and Lookback Options Via Laplace Transforms. Journal of Computational Finance, vol. 8, 2004, pp. 1-37. [PDF]

Markov Chain Tools

• Examples of transition matrices constructed in MATLAB:

  • two-state example (in PDF)

  • six-state example (in PDF)

  • magic-square example (in PDF)

    (doubly stochastic example)

  • five-state example (in PDF)

    (classifying states)

  • seven-state example (in PDF)

    (classifying states)

• Markov Chain Programs and Data for MATLAB:

  • (stationary) Markov Mouse Example (PDF) (See Class Lecture Notes for 2/3.)

    Markov Mouse data (to use as input to MATLAB using load command)

    stationary vector MATLAB programs: stat.m (PDF version) and stationary.m (PDF version)

    Escaping Mouse Example(PDF)

    Escaping Mouse Q data (to use as input to MATLAB)

    Escaping Mouse R data (to use as input to MATLAB)

    absorbing Markov chain MATLAB program: absorbing.m (PDF version)

    six-state periodic chain example (PDF)

    data for six-state periodic example (to use as input to MATLAB)