rpylib

Scope

This Python pricing library was developed as a companion code for the paper:
"A Weak MLMC Scheme for Lévy-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(v_l), the log level variances in function of the level l
• log₂|m_l| the log level means in function of the level l
• N_l (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:

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]: Lévy Copulas: Review of Recent Results, P. Tankov
[2]: A Structural Jump Threshold Framework for Credit Risk, P. Garreau, A. Kercheval
[3]: Multilevel Monte Carlo Path Simulation, M.B. Giles
[4]: Multilevel Monte Carlo methods, M.B. Giles

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Contact:

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