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 X(t) | X(0) = x_0
of the Black-Scholes-Merton process
also known as the 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 |
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 |
lower.tail |
logical; if TRUE (default), probabilities are |
Details
This function returns quantities related to the conditional law of the process solution of
{\rm d}X_t = \theta_1 X_t {\rm d}t + \theta_2 X_t {\rm d}W_t.
Constraints: \theta_3>0
.
Value
x |
a numeric vector |
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))