DjvKdZddlZddlmZmZddlmZGddZ Gdde Z Gdd e Z Gd d e Z Gd d e Z Gdde ZGdde ZGddZGddZ edk(rdZdZgZdevr e Zej/deZerhej2ej4edj6Zej4edj;ddZej<ddZejAede Z!erYej2ej4e!dj6Zej4e!ddZej<d!ejDjGe!dejHd"e!dzd#z z ejJZ&e'e&e d$d%d&'Z(e(jSd(d( Z*erej2ej4e*j6Zej4e*j;ddZej<d)ej2ej4ejVe*j6Zej4ejVe*j;ddZej<d*e dd+d'Z,e,jSd(d( Z-erbej2ej4e-j6Zej4e-j;ddZej<d,eddd&d-.Z.e.jSZ/e.jaddejbjed/0Z3e.jadejhdd1d2de.jkdd1e'e.jkdd1d-d13j;de.jkdd(d-d(3Z6erbej2ej4e6j6Zej4e6j;ddZej<d4eddd&d-5Z7e7jkdd6d-d(3Z8e'e8j;de'ejVe8j;ddZerbej2ej4e8j6Zej4e8j;ddZej<d7e'e7jse8dddfd-8e7jkddd-d93Z:e'd:e;d9D]Z<e'e7jse:e<d-8 eZ=e=j}dd&d;dd$d-<\Z?Z@ZAerej2ej4e?j6Zej4e?j;ddZej<d=ej2ej4eAd>d?@ej4e?jddA@ej<dBejeddgejbjdejbjdgZDeDj}dCdD ZEe'eEdjdEjdEe'eEdje'eEdj;dEj;dEe'eEdj;e'eEdje'eEdjyy)Fa6getting started with diffusions, continuous time stochastic processes Author: josef-pktd License: BSD References ---------- An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations Author(s): Desmond J. Higham Source: SIAM Review, Vol. 43, No. 3 (Sep., 2001), pp. 525-546 Published by: Society for Industrial and Applied Mathematics Stable URL: http://www.jstor.org/stable/3649798 http://www.sitmo.com/ especially the formula collection Notes ----- OU process: use same trick for ARMA with constant (non-zero mean) and drift some of the processes have easy multivariate extensions *Open Issues* include xzero in returned sample or not? currently not *TODOS* * Milstein from Higham paper, for which processes does it apply * Maximum Likelihood estimation * more statistical properties (useful for tests) * helper functions for display and MonteCarlo summaries (also for testing/checking) * more processes for the menagerie (e.g. from empirical papers) * characteristic functions * transformations, non-linear e.g. log * special estimators, e.g. Ait Sahalia, empirical characteristic functions * fft examples * check naming of methods, "simulate", "sample", "simexact", ... ? stochastic volatility models: estimation unclear finance applications ? 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