Value at Risk Calculation in Lognormal Approximation

VaR.norm {VaR}

R Documentation

Value at Risk Calculation in Lognormal Approximation

Description

This function estimates Value of Risk (VaR) value in lognormal approximation.

Usage

VaR.norm(ydat, p = 0.99, dt = 1, type = "long", drift.appx = FALSE, lin.appx = TRUE)

Arguments

ydat	Numeric vector of data for which VaR is to be calculated
p	Confidence level for VaR calculation
dt	Liquidation period
type	String describing type of VaR calculated: "long" or "short"
drift.appx	Logical; if TRUE VaR is calculated in non-zero drift approximation
lin.appx	Logical; if TRUE VaR is calculated in linear approximation

Details

This function estimates VaR for a single risk factor S(t) in lognormal approximation. The final expression for VaR of {bf long} and {bf short} position is

VaR_{long}(c)=S(t)[1-exp(μ delta t + Q^{N(0,1)}_{1-c} σ sqrt{delta t})]

VaR_{short}(c)=-S(t)[1-exp(μ delta t - Q^{N(0,1)}_{1-c} σ sqrt{delta t})]

Here, c is a desired confidence, Q^{N(0,1)}_{1-c} is a 1-c percentile of normal distribution, delta t is liquidation period, and parameters μ and σ are mean value (or drift) and standard deviation of delta S(t). If drift.appx=FALSE, μ = 0. If lin.appx=TRUE, the above functions are expanded according exp(x) = 1+x.

Value

Return value is a list containing following components:

VaR	Value at Risk for input data
data	Input data
cdata	Log-transformed data
liq.period	Same as dt
type	Same as type
conf.level	Same as p
mean	Mean value of cdata
std	Standard deviation of cdata

Author(s)

T. Daniyarov

References

Deutsch, H.P., Derivatives and Internal Models, 2nd Edition, Palgrave, London 2001

See Also

VaR.norm.plots, VaR.backtest

Examples

data(exchange.rates)
attach(exchange.rates)
y <- USDJPY[!is.na(USDJPY)]
z <- VaR.norm(y)
z$VaR
detach(exchange.rates)

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[Package VaR version 0.2 Index]