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DROP Dynamics

DROP Dynamics contains implementations of the HJM, Hull White, LMM, and SABR Dynamic Evolution Models.

Component Packages

  • Evolution DROP Dynamics Evolution Package implements the Latent State Evolution Edges/Vertexes.

  • HJM DROP Dynamics HJM Package implements the HJM Based Latent State Evolution.

  • Hull White DROP Dynamics Hull White Package implements the Hull White Latent State Evolution.

  • Ito DROP Dynamics Ito Package implements the Ito Stochastic Process Dynamics Foundation.

  • Kolmogorov DROP Dynamics Kolmogorov Package implements Fokker Planck Kolmogorov Forward/Backward Equations.

  • LMM DROP Dynamics LMM Package implements the LMM Based Latent State Evolution.

  • Mean Reverting DROP Dynamics Mean Reverting Package implements the Mean Reverting Stochastic Process Dynamics.

  • Physical DROP Dynamics Physical Package contains the Implementation of Physical Process Dynamics.

  • Process DROP Dynamics Process Package implements Ito-Dynamics Based Stochastic Process.

  • SABR DROP Dynamics SABR Package implements the SABR Based Latent State Evolution.

References

  • Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics Russian Mathematical Surveys 49 (5) 19-49

  • Brace, A., D. Gatarek, and M. Musiela (1997): The Market Model of Interest Rate Dynamics Mathematical Finance 7 (2) 127-155

  • Doob, J. L. (1942): The Brownian Movement and Stochastic Equations Annals of Mathematics 43 (2) 351-369

  • Gardiner, C. W. (2009): Stochastic Methods: A Handbook for the Natural and Social Sciences 4th Edition Springer Verlag

  • Goldys, B., M. Musiela, and D. Sondermann (1994): Log-normality of Rates and Term Structure Models The University of New South Wales

  • Heath, D., R. Jarrow, and A. Morton (1992): Bond Pricing and Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation Econometrica 60 (1) 77-105

  • Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for Time-dependent Fokker-Planck Equations Physical Review E 99 (4) 032117

  • Kadanoff, L. P. (2000): Statistical Physics: Statics, Dynamics, and Renormalization World Scientific

  • Karatzas, I., and S. E. Shreve (1991): Brownian Motion and Stochastic Calculus 2nd Edition Springer Verlag

  • Musiela, M. (1994): Nominal Annual Rates and Log-normal Volatility Structure The University of New South Wales

  • Ottinger, H. C. (1996): Stochastic Processes in Polymeric Fluids Springer-Verlag Berlin-Heidelberg

  • Risken, H., and F. Till (1996): The Fokker Planck Equation; Methods of Solution and Applications Springer

  • Wikipedia (2019): Fokker-Planck Equation https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation

DROP Specifications