rmilstein: Milstein Scheme for Stochastic Differential Equations

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 Milstein Scheme is X[t+h] = X[t] + b(X[t])h + s(X[t])Z + 0.5*s'(X[t])*(Z^2 - h), where Z ~ N(0,h) (variance h), and s' is the differential function of s.

Usage

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

Arguments

integer, number of paths.

integer, number of steps, the step size will be T/m.

numeric, starting point of the process.

function, the drift, a function which can take a vector and returns a vector.

function, the volatility, a function which can take a vector and returns a vector.

function, the differential of the volatility, a function which can take a vector and returns a vector.

double, the starting date of the process.

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.

References

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

Examples

Run this code

# NOT RUN {
mu <- 0.07
sigma <- 0.20
rmilstein(5, 10, 1, function(x) return(mu*x),
	function(x) return(sigma*x), function(x) return(sigma))
# }