rcBS | R Documentation |
Density, distribution function, quantile function, and random generation for the conditional law X(t) | X(0) = x0 of the Black-Scholes-Merton process also known as the 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 |
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 |
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 |
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))
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