ghyp: ghyp-risk-performance – R documentation

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ghyp-risk-performance

Risk and Performance Measures

Description

Functions to compute the risk measure Expected Shortfall and the performance measure Omega based on univariate generalized hyperbolic distributions.

Usage

ESghyp(alpha, object = ghyp(), distr = c("return", "loss"), ...)

ghyp.omega(L, object = ghyp(), ...)

Arguments

`alpha`	A vector of confidence levels.
`L`	A vector of threshold levels.
`object`	A univarite generalized hyperbolic distribution object inheriting from class `ghyp`.
`distr`	Whether the ghyp-object specifies a return or a loss-distribution (see Details).
`...`	Arguments passed from `ESghyp` to `qghyp` and from `ghyp.omega` `integrate`.

Details

The parameter distr specifies whether the ghyp-object describes a return or a loss-distribution. In case of a return distribution the expected-shortfall on a confidence level alpha is defined as ES_alpha := E(X | X <= F^-1(alpha)) while in case of a loss distribution it is defined on a confidence level alpha as ES_alpha := E(X | X > F^-1(alpha)).

Omega is defined as the ratio of a European call-option price divided by a put-option price with strike price L (see References): Omega(L) = C(L)/P(L).

Value

ESghyp gives the expected shortfall and
ghyp.omega gives the performance measure Omega.

Author(s)

David Luethi

References

Omega as a Performance Measure by Hossein Kazemi, Thomas Schneeweis and Raj Gupta
University of Massachusetts, 2003

Examples

data(smi.stocks)

  ## Fit a NIG model to Credit Suisse and Swiss Re log-returns
  cs.fit <- fit.NIGuv(smi.stocks[, "CS"], silent = TRUE)
  swiss.re.fit <- fit.NIGuv(smi.stocks[, "Swiss.Re"], silent = TRUE)

  ## Confidence levels for expected shortfalls
  es.levels <- c(0.001, 0.01, 0.05, 0.1)

  cs.es <- ESghyp(es.levels, cs.fit)
  swiss.re.es <- ESghyp(es.levels, swiss.re.fit)

  ## Threshold levels for Omega
  threshold.levels <- c(0, 0.01, 0.02, 0.05)

  cs.omega <- ghyp.omega(threshold.levels, cs.fit)
  swiss.re.omega <- ghyp.omega(threshold.levels, swiss.re.fit)

  par(mfrow = c(2, 1))

  barplot(rbind(CS = cs.es, Swiss.Re = swiss.re.es), beside = TRUE,
          names.arg = paste(100 * es.levels, "percent"), col = c("gray40", "gray80"),
          ylab = "Expected Shortfalls (return distribution)", xlab = "Level")

  legend("bottomright", legend = c("CS", "Swiss.Re"), fill = c("gray40", "gray80"))

  barplot(rbind(CS = cs.omega, Swiss.Re = swiss.re.omega), beside = TRUE,
          names.arg = threshold.levels, col = c("gray40", "gray80"),
          ylab = "Omega", xlab = "Threshold level")
  legend("topright", legend = c("CS", "Swiss.Re"), fill = c("gray40", "gray80"))

  ## => the higher the performance, the higher the risk (as it should be)

ghyp

Generalized Hyperbolic Distribution and Its Special Cases

v1.6.1

GPL (>= 2)

Authors

Marc Weibel, David Luethi, Wolfgang Breymann

Initial release

2020-04-27