OUstepEuler: Generate the next element based on Ornstein-Uhlenbeck process...

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

Description

Generate the next element based on Ornstein-Uhlenbeck process using antithetic concept and assuming that the Brownian motion has Euler discretization

Usage

  OUstepEuler(X_0, Dt, Mu, Th, Sig)

Arguments

X_0	a matrix containing the starting value of each process
Dt	a numeric containing the timestep
Mu	a vector containing the unconditional expectation of the process
Th	a transition matrix, i.e., a fully generic square matrix that steers the deterministic portion of the evolution of the process
Sig	a square matrix that drives the dispersion of the process

Value

a list containing

X_t a vector containing the value of the process after the given timestep

Mu_t a vector containing the conditional expectation of the process

Sig_t a matrix containing the covariance after the time step

X_{t+ τ } = \big(I- e^{- θ τ } \big) μ + e^{- θ τ } X_{t} + ε _{t, τ }

Author(s)

Manan Shah [e-mail]

References

A. Meucci - "Review of Statistical Arbitrage, Cointegration, and Multivariate Ornstein-Uhlenbeck" - Formula (2) http://ssrn.com/abstract=1404905

R-Finance/Meucci documentation built on May 8, 2019, 3:52 a.m.