rcBS {sde} | R Documentation |
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
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)
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]. |
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
.
x |
a numeric vector |
This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.
Stefano Maria Iacus
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.
rcBS(n=1, Dt=0.1, x0=1, theta=c(2,1))