rcBS {sde}R Documentation

Black-Scholes-Merton or Geometric Brownian Motion process conditional law

Description

Density, distribution function, quantile function and random generation for the conditional law Xt|X0=x0 of the Black-Scholes-Merton process also known as Geometric Brownian Motion process

Usage

dcBS(x, Dt, x0, theta, log = FALSE)
pcBS(x, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE) 
qcBS(p, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE)
rcBS(n=1, Dt, x0, theta)

Arguments

x vector of quantiles.
p vector of probabilities.
Dt lag or time
x0 the value of the process at time t. See details.
theta parameter of the Black-Scholes-Merton process. See details.
n number of random numbers to generate from the conditional distribution.
log, log.p logical; if TRUE, probabilities p are given as log(p).
lower.tail logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x].

Details

This function returns quantities related to the conditional law of the process solution of dX_t = theta[1]*Xt*dt + theta[2]*Xt*dWt.

Constraints: theta[3]>0.

Value

x a numeric vector

Note

This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.

Author(s)

Stefano Maria Iacus

References

Black, F., Scholes, M.S. (1973) The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637-654.

Merton, R. C. (1973) Theory of rational option pricing, Bell Journal of Economics and Management Science, 4(1), 141-183.

Examples

rcBS(n=1, Dt=0.1, x0=1, theta=c(2,1))

[Package sde version 1.9.14 Index]