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rpylib

Multilevel Monte-Carlo simulation of Lévy-driven SDEs via a Continuous-Time Markov Chain approximation

https://github.com/rpalfray/rpylib

Science Score: 49.0%

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    Links to: springer.com
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Keywords

levy-copula levy-driven-sde markov-chain multilevel-monte-carlo python
Last synced: 6 months ago · JSON representation

Repository

Multilevel Monte-Carlo simulation of Lévy-driven SDEs via a Continuous-Time Markov Chain approximation

Basic Info
  • Host: GitHub
  • Owner: rpalfray
  • License: gpl-3.0
  • Language: Python
  • Default Branch: master
  • Homepage:
  • Size: 598 KB
Statistics
  • Stars: 6
  • Watchers: 1
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Topics
levy-copula levy-driven-sde markov-chain multilevel-monte-carlo python
Created over 3 years ago · Last pushed about 1 year ago
Metadata Files
Readme License Citation

README.md

rpylib

Documentation Status Build Status Code style: black

Scope

This Python pricing library was developed as a companion code for the paper:
"A Weak MLMC Scheme for Lvy-copula-driven SDEs with Applications to the Pricing of Credit, Equity and Interest Rate Derivatives".

The results consist of the numerical analysis of: - the benchmark of the Continuous-Time Markov Chain (CTMC) scheme approximation against the series representation[1] - the benchmark of the CTMC scheme against the closed-form formula for First-to-Default CDS[2] - the weak and strong convergence of the multilevel CTMC scheme as well as the convergence rate of the cost w.r.t the rmse compared to the standard Monte-Carlo; these results mimic those of Giles[3][4] for diffusion processes
The different convergence rates considered in our case are dependent on the Blumenthal-Getoor index of the underlying Levy process.

Results

The main results are presented in the form of 4 graphs (as in Giles[3][4]):
- log2(vl), the log level variances in function of the level l - log2|ml| the log level means in function of the level l - Nl (optimal number of Monte-Carlo paths for the level l) in function of the level l - the total costs of the multilevel Monte-Carlo and the standard Monte-Carlo in function of the rmse (root-mean square error)

MLMC applied to CGMY with beta=1.5:

MLMC applied to CGMY with beta=1.5

Scripts

For the paper:

See the slurm folder.

Additional scripts:

Other scripts are available in scripts/statistics. These scripts allow to plot the distribution of the spot underlying of the Levy process simulated by Monte-Carlo (either directly from the SDE or from the CTMC scheme).

[1]: [Lvy Copulas: Review of Recent Results](https://link.springer.com/chapter/10.1007/978-3-319-25826-37), P. Tankov
[2]: _A Structural Jump Threshold Framework for Credit Risk, P. Garreau, A. Kercheval
[3]: [Multilevel Monte Carlo Path Simulation](https://people.maths.ox.ac.uk/gilesm/files/OPRE2008.pdf), M.B. Giles
[4]: _Multilevel Monte Carlo methods, M.B. Giles

Contact:

Any feedback on this project will be appreciated, please log a new Issue or email me.

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Dependencies

.github/workflows/black.yml actions
  • actions/checkout v2 composite
  • psf/black stable composite
.github/workflows/codeql-analysis.yml actions
  • actions/checkout v3 composite
  • github/codeql-action/analyze v2 composite
  • github/codeql-action/autobuild v2 composite
  • github/codeql-action/init v2 composite
requirements.txt pypi
rpylib/distribution/univariate/poisson_impl/setup.py pypi
setup.py pypi