reuler: Euler Scheme for Stochastic Differential Equations

In rpgm: Fast Simulation of Normal/Exponential Random Variables and Stochastic Differential Equations / Poisson Processes

Description

If the process X_t is the unique strong solution of the process

dX_t = b(X_t)dt + s(X_t)dW_t,

then the Euler Scheme is X[t+h] = X[t] + b(X[t])h + s(X[t])sqrt(h)Z, where Z ~ N(0,1).

Usage

reuler(n, m, x0, b, s, t0 = 0, T = 1, all_dates = TRUE, delta = NULL)

Arguments

n	integer, number of paths.
m	integer, number of steps, the step size will be T/m.
x0	numeric, starting point of the process.
b	function, the drift, a function which can take a vector and returns a vector.
s	function, the volatility, a function which can take a vector and returns a vector.
t0	double, the starting date of the process.
T	double, the final date of the process.
all_dates	logical, if TRUE, returns all steps from all paths. If FALSE, only returns the n final value X_T.
delta	double, the step size.

Value

If all_dates = TRUE, it returns a n x m+1 matrix : n paths with m steps (+ the first value). Else, it returns a vector of length n with the simulations of the final dates X_T.

Author(s)

Nicolas Baradel - PGM Solutions

References

https://en.wikipedia.org/wiki/Euler

See Also

https://pgm-solutions.com/packages

Examples

mu <- 0.07
sigma <- 0.20
reuler(5, 10, 1, function(x) return(mu*x), function(x) return(sigma*x))

rpgm documentation built on March 18, 2018, 2:24 p.m.