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Functions for Scenario Analysis and Risk Management

Oftentimes, the econometrician needs to stress-test the potentialoutcomes for a given set of risk-drivers. This process can becomputationally costly when the entire set of scenarios needs to berepriced.

To overcome this difficulty, the Fully Flexible Probabilities (FFP)approach offers an inexpensive way for scenario generation: it repricestheprobabilities associated to each scenario, instead of thescenarios themselves. Once the new probabilities have been defined, thecomputations can be performed very quickly because the burden ofscenario generation has been left aside.

Install the official version from CRAN with:

install.packages("ffp")

Install the development version from github with:

# install.packages("devtools")devtools::install_github("Reckziegel/ffp")

The packageffp comes with five functions to extract probabilitiesfrom the historical scenarios:

• exp_decay(): accounts for the time-changing nature of volatilityby giving more weight to recent observations;
• crisp(): selects scenarios where a logical statement is satisfied;
• kernel_normal(): generalizes thecrisp condition by wrappingscenarios over a normal kernel;
• kernel_entropy(): uses entropy-polling to satisfy a conditioningstatement;
• double_decay(): uses entropy-polling and a double-decay factor toconstrain the first two moments of a distribution.

The package also offers eight different constructors to make it easierto input views on the market for portfolio optimization (mean-variance,risk-parity, etc.):

• view_on_mean()
• view_on_covariance()
• view_on_correlation()
• view_on_volatility()
• view_on_rank()
• view_on_copula()
• view_on_marginal_distribution()
• view_on_joint_distribution()

The output is a list thatentropy_pooling() can handle easily. Tocombine multiple views in a single object usebind_views().

Once the new probabilities have been estimated,bootstrap_scenarios()can be used to sample data, while keeping the structure of the empiricalcopulas intact.

The main statistics of arbitrary scenarios can be computed withempirical_stats().

• Attilio Meucci (2021). Historical Scenarios with Fully FlexibleProbabilities(https://www.mathworks.com/matlabcentral/fileexchange/31360-historical-scenarios-with-fully-flexible-probabilities),MATLAB Central File Exchange. Retrieved June 11, 2021.

• De Santis, G., R. Litterman, A. Vesval, and K. Winkelmann, 2003,Covariance matrix estimation, Modern investment management: anequilibrium approach, Wiley.

• Meucci, Attilio, Fully Flexible Views: Theory and Practice (August8, 2008). Fully Flexible Views: Theory and Practice, Risk, Vol. 21,No. 10, pp. 97-102, October 2008, Available at SSRN:https://www.ssrn.com/abstract=1213325

• Meucci, Attilio, Historical Scenarios with Fully FlexibleProbabilities (October 23, 2010). GARP Risk Professional, pp. 47-51,December 2010, Available at SSRN:https://www.ssrn.com/abstract=1696802 orhttp://dx.doi.org/10.2139/ssrn.1696802