NNS rescale

Rescale a vector using either min-max scaling or risk-neutral adjustment.

Usage

NNS.rescale(x, a, b, method = "minmax", T = NULL, type = "Terminal")

Arguments

x

numeric vector; data to rescale (e.g., terminal prices for risk-neutral method).

a

numeric; defines the scaling target: - For method = "minmax": the lower limit of the output range (e.g., 5 to scale to [5, b]). - For method = "riskneutral": the initial price \( S_0 \) (must be positive, e.g., 100), used to set the target mean.

b

numeric; defines the scaling range or rate: - For method = "minmax": the upper limit of the output range (e.g., 10 to scale to [a, 10]). - For method = "riskneutral": the risk-free rate \( r \) (e.g., 0.05), used with \( T \) to adjust the mean.

method

character; scaling method: "minmax" (default) for min-max scaling, or "riskneutral" for risk-neutral adjustment.

T

numeric; time to maturity in years (required for method = "riskneutral", ignored otherwise; e.g., 1). Default is NULL.

type

character; for method = "riskneutral": "Terminal" (default) or "Discounted" (mean = \( S_0 \)).

Value

Returns a rescaled distribution: - For "minmax": values scaled linearly to the range [a, b]. - For "riskneutral": values scaled multiplicatively to a risk-neutral mean (\( S_0 e^(rT) \) if type = "Terminal", or \( S_0 \) if type = "Discounted").

Author

Fred Viole, OVVO Financial Systems

Examples

if (FALSE) { # \dontrun{
set.seed(123)
# Min-max scaling: a = lower limit, b = upper limit
x <- rnorm(100)
NNS.rescale(x, a = 5, b = 10, method = "minmax")  # Scales to [5, 10]

# Risk-neutral scaling (Terminal): a = S_0, b = r  # Mean approx 105.13
prices <- 100 * exp(cumsum(rnorm(100, 0.001, 0.02)))
NNS.rescale(prices, a = 100, b = 0.05, method = "riskneutral", T = 1, type = "Terminal")

# Risk-neutral scaling (Discounted): a = S_0, b = r  # Mean approx 100
NNS.rescale(prices, a = 100, b = 0.05, method = "riskneutral", T = 1, type = "Discounted")
} # }