467 research outputs found
Calculation of aggregate loss distributions
Estimation of the operational risk capital under the Loss Distribution
Approach requires evaluation of aggregate (compound) loss distributions which
is one of the classic problems in risk theory. Closed-form solutions are not
available for the distributions typically used in operational risk. However
with modern computer processing power, these distributions can be calculated
virtually exactly using numerical methods. This paper reviews numerical
algorithms that can be successfully used to calculate the aggregate loss
distributions. In particular Monte Carlo, Panjer recursion and Fourier
transformation methods are presented and compared. Also, several closed-form
approximations based on moment matching and asymptotic result for heavy-tailed
distributions are reviewed
Percentiles of sums of heavy-tailed random variables: Beyond the single-loss approximation
The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-013-9376-6A perturbative approach is used to derive
approximations of arbitrary order to estimate high percentiles
of sums of positive independent random variables
that exhibit heavy tails. Closed-form expressions
for the successive approximations are obtained both
when the number of terms in the sum is deterministic
and when it is random. The zeroth order approximation
is the percentile of the maximum term in the
sum. Higher orders in the perturbative series involve
the right-truncated moments of the individual random
variables that appear in the sum. These censored moments
are always finite. As a result, and in contrast
to previous approximations proposed in the literature,
the perturbative series has the same form regardless of
whether these random variables have a finite mean or
not. For high percentiles, and specially for heavier tails,
the quality of the estimate improves as more terms are
included in the series, up to a certain order. Beyond
that order the convergence of the series deteriorates.
Nevertheless, the approximations obtained by truncating
the perturbative series at intermediate orders are
remarkably accurate for a variety of distributions in a
wide range of parameters.The authors thank the anonymous reviewers
for their valuable comments and suggestions. A.S.
acknowledges financial support from the Spanish Dirección
General de Investigación, project TIN2010-21575-C02-02
Jump-diffusion model of exchange rate dynamics : estimation via indirect inference
This paper investigates asymmetric effects of monetary policy over the business cycle. A two-state Markov Switching Model is employed to model both recessions and expansions. For the United States and Germany, strong evidence is found that monetary policy is more effective in a recession than during a boom. Also some evidence is found for asymmetry in the United Kingdom and Belgium. In the Netherlands, monetary policy is not very effective in either regime.
Implementing Loss Distribution Approach for Operational Risk
To quantify the operational risk capital charge under the current regulatory
framework for banking supervision, referred to as Basel II, many banks adopt
the Loss Distribution Approach. There are many modeling issues that should be
resolved to use the approach in practice. In this paper we review the
quantitative methods suggested in literature for implementation of the
approach. In particular, the use of the Bayesian inference method that allows
to take expert judgement and parameter uncertainty into account, modeling
dependence and inclusion of insurance are discussed
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