Methodology

Bibliography

Every model in the Prometheus engine is built on standard, peer-reviewed methods from the open econometrics, statistics, and actuarial literature. These are the primary sources, the GARCH and density-estimation papers behind the market models, the distributional families behind the fat tails, and the rank-correlation and goodness-of-fit methods behind the simulation. For how they fit together, see the methodology.

24 sources
  1. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171–178.
    jstor.org/stable/4615982
  2. Barndorff-Nielsen, O. E. (1997). Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics, 24(1), 1–13.
    https://doi.org/10.1111/1467-9469.00045
  3. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.
    https://doi.org/10.1016/0304-4076(86)90063-1
  4. Bollerslev, T. (1987). A conditionally heteroskedastic time series model for speculative prices and rates of return. The Review of Economics and Statistics, 69(3), 542–547.
    https://doi.org/10.2307/1925546
  5. Boyle, P. P. (1977). Options: A Monte Carlo approach. Journal of Financial Economics, 4(3), 323–338.
    https://doi.org/10.1016/0304-405X(77)90005-8
  6. Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (1984). Classification and Regression Trees. Wadsworth.
    ISBN 978-0-412-04841-8
  7. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987–1007.
    https://doi.org/10.2307/1912773
  8. Frachot, A., Georges, P., & Roncalli, T. (2001). Loss distribution approach for operational risk. Groupe de Recherche Opérationnelle, Crédit Lyonnais.Working paper
    https://doi.org/10.2139/ssrn.1032523
  9. Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. Springer.
    https://doi.org/10.1007/978-0-387-21617-1
  10. Hansen, B. E. (1994). Autoregressive conditional density estimation. International Economic Review, 35(3), 705–730.
    https://doi.org/10.2307/2527081
  11. Higham, N. J. (2002). Computing the nearest correlation matrix—A problem from finance. IMA Journal of Numerical Analysis, 22(3), 329–343.
    https://doi.org/10.1093/imanum/22.3.329
  12. Iman, R. L., & Conover, W. J. (1982). A distribution-free approach to inducing rank correlation among input variables. Communications in Statistics – Simulation and Computation, 11(3), 311–334.
    https://doi.org/10.1080/03610918208812265
  13. Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36(1/2), 149–176.
    https://doi.org/10.1093/biomet/36.1-2.149
  14. Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81–93.
    https://doi.org/10.1093/biomet/30.1-2.81
  15. Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2012). Loss Models: From Data to Decisions (4th ed.). Wiley.
    ISBN 978-1-118-31532-3
  16. Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell'Istituto Italiano degli Attuari, 4, 83–91.
  17. Litterman, R., & Scheinkman, J. (1991). Common factors affecting bond returns. The Journal of Fixed Income, 1(1), 54–61.
    https://doi.org/10.3905/jfi.1991.692347
  18. Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303.
    https://doi.org/10.1093/biomet/65.2.297
  19. McDonald, J. B. (1984). Some generalized functions for the size distribution of income. Econometrica, 52(3), 647–663.
    https://doi.org/10.2307/1913469
  20. McDonald, J. B., & Xu, Y. J. (1995). A generalization of the beta distribution with applications. Journal of Econometrics, 66(1–2), 133–152.
    https://doi.org/10.1016/0304-4076(94)01612-4
  21. Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 5, 50(302), 157–175.
    https://doi.org/10.1080/14786440009463897
  22. Rebonato, R., & Jäckel, P. (2000). The most general methodology for creating a valid correlation matrix for risk management and option pricing purposes. Journal of Risk, 2(2), 17–27.
    risk.net
  23. Smirnov, N. (1948). Table for estimating the goodness of fit of empirical distributions. Annals of Mathematical Statistics, 19(2), 279–281.
    https://doi.org/10.1214/aoms/1177730256
  24. Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15(1), 72–101.
    https://doi.org/10.2307/1412159