Yuima : the project for simulation and inference of multi-dimensional stochastic differential equations

Most of the theoretical results in modern finance rely on the assumption that the underlying dynamics of asset prices, currencies exchange rates, interest rates, etc are continuous time stochastic processes driven by stochastic differential equations. Continuous time models are also at the basis of option pricing and option pricing often requires Monte Carlo methods. In turn, the Monte Carlo method requires a preliminary good model to simulate whose parameters has to be estimated from historical data. Most ready-to-use tools in computational finance relies on pure discrete time models, like arch, garch, etc. and very few examples of software handling continuous time processes in a general fashion are available also in the R community. There still exists a gap between what is going on in mathematical finance and applied finance. The "yuima" package is intended to help in filling this gap. The Yuima Project is an open source and collaborative effort of several mathematicians and statisticians aimed at developing the R package named "yuima" for simulation and inference of stochastic differential equations. The "yuima" package is an environment that follows the paradigm of methods and classes of the S4 system for the R language. In the "yuima" package stochastic differential equations can be of very abstract type, e.g. uni or multidimensional, driven by Wiener process of fractional Brownian motion with general Hurst parameter, with or without jumps specified as L .A Nivy noise. L Nivy processes can be specified via compound Poisson description, by the specification of the L Nivy measure or via increments and stable laws. The "yuima" package is intended to offer the basic infrastructure on which complex models and inference procedures can be built on. In particular, the basic set of functions includes the following: 1) Simulation schemes for all types of stochastic differential equations (Wiener, fBm, L .A Nivy). 2) Different subsampling schemes including random sampling with user specified random times distribution, space discretization, tick times, etc. 3) Automatic asymptotic expansion for the approximation and estimation of functionals of diffusion processes with small noise via Malliavin calculus, useful in option pricing. 4) Efficient quasi-likelihood inference for diffusion processes and diffusion processes with jumps; 5) changepoint analysis, etc. All simulation schemes, subsampling and inference are designed to work on both regular or irregular grid times (i.e. regular or irregular time series). In special cases also asynchronous data and sampling schemes can be handled