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Calibration of VaR models with overlapping data
- Ralph Frankland, Andrew D. Smith, James Sharpe, Rishi Bhatia, Stuart Jarvis, Parit Jakhria, Gaurang Mehta
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- Journal:
- British Actuarial Journal / Volume 24 / 2019
- Published online by Cambridge University Press:
- 26 July 2019, e23
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Under the European Union’s Solvency II regulations, insurance firms are required to use a one-year VaR (Value at Risk) approach. This involves a one-year projection of the balance sheet and requires sufficient capital to be solvent in 99.5% of outcomes. The Solvency II Internal Model risk calibrations require annual changes in market indices/term structure for the estimation of risk distribution for each of the Internal Model risk drivers. This presents a significant challenge for calibrators in terms of:
Robustness of the calibration that is relevant to the current market regimes and at the same time able to represent the historically observed worst crisis;
Stability of the calibration model year on year with arrival of new information.
The above points need careful consideration to avoid credibility issues with the Solvency Capital Requirement (SCR) calculation, in that the results are subject to high levels of uncertainty.
For market risks, common industry practice to compensate for the limited number of historic annual data points is to use overlapping annual changes. Overlapping changes are dependent on each other, and this dependence can cause issues in estimation, statistical testing, and communication of uncertainty levels around risk calibrations.
This paper discusses the issues with the use of overlapping data when producing risk calibrations for an Internal Model. A comparison of the overlapping data approach with the alternative non-overlapping data approach is presented. A comparison is made of the bias and mean squared error of the first four cumulants under four different statistical models. For some statistical models it is found that overlapping data can be used with bias corrections to obtain similarly unbiased results as non-overlapping data, but with significantly lower mean squared errors. For more complex statistical models (e.g. GARCH) it is found that published bias corrections for non-overlapping and overlapping datasets do not result in unbiased cumulant estimates and/or lead to increased variance of the process.
In order to test the goodness of fit of probability distributions to the datasets, it is common to use statistical tests. Most of these tests do not function when using overlapping data, as overlapping data breach the independence assumption underlying most statistical tests. We present and test an adjustment to one of the statistical tests (the Kolmogorov Smirnov goodness-of-fit test) to allow for overlapping data.
Finally, we explore the methods of converting “high”-frequency (e.g. monthly data) to “low”-frequency data (e.g. annual data). This is an alternative methodology to using overlapping data, and the approach of fitting a statistical model to monthly data and then using the monthly model aggregated over 12 time steps to model annual returns is explored. There are a number of methods available for this approach. We explore two of the widely used approaches for aggregating the time series.
Clinical predictors of conversion to bipolar disorder in a prospective longitudinal familial high-risk sample: focus on depressive features
- Andrew Frankland, Gloria Roberts, Ellen Holmes-Preston, Tania Perich, Florence Levy, Rhoshel Lenroot, Dusan Hadzi-Pavlovic, Michael Breakspear, Philip B. Mitchell
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- Journal:
- Psychological Medicine / Volume 48 / Issue 10 / July 2018
- Published online by Cambridge University Press:
- 07 November 2017, pp. 1713-1721
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Background
Identifying clinical features that predict conversion to bipolar disorder (BD) in those at high familial risk (HR) would assist in identifying a more focused population for early intervention.
MethodIn total 287 participants aged 12–30 (163 HR with a first-degree relative with BD and 124 controls (CONs)) were followed annually for a median of 5 years. We used the baseline presence of DSM-IV depressive, anxiety, behavioural and substance use disorders, as well as a constellation of specific depressive symptoms (as identified by the Probabilistic Approach to Bipolar Depression) to predict the subsequent development of hypo/manic episodes.
ResultsAt baseline, HR participants were significantly more likely to report ⩾4 Probabilistic features (40.4%) when depressed than CONs (6.7%; p < .05). Nineteen HR subjects later developed either threshold (n = 8; 4.9%) or subthreshold (n = 11; 6.7%) hypo/mania. The presence of ⩾4 Probabilistic features was associated with a seven-fold increase in the risk of ‘conversion’ to threshold BD (hazard ratio = 6.9, p < .05) above and beyond the fourteen-fold increase in risk related to major depressive episodes (MDEs) per se (hazard ratio = 13.9, p < .05). Individual depressive features predicting conversion were psychomotor retardation and ⩾5 MDEs. Behavioural disorders only predicted conversion to subthreshold BD (hazard ratio = 5.23, p < .01), while anxiety and substance disorders did not predict either threshold or subthreshold hypo/mania.
ConclusionsThis study suggests that specific depressive characteristics substantially increase the risk of young people at familial risk of BD going on to develop future hypo/manic episodes and may identify a more targeted HR population for the development of early intervention programs.
Comparison of depressive episodes in bipolar disorder and in major depressive disorder within bipolar disorder pedigrees
- Philip B. Mitchell, Andrew Frankland, Dusan Hadzi-Pavlovic, Gloria Roberts, Justine Corry, Adam Wright, Colleen K. Loo, Michael Breakspear
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- Journal:
- The British Journal of Psychiatry / Volume 199 / Issue 4 / October 2011
- Published online by Cambridge University Press:
- 02 January 2018, pp. 303-309
- Print publication:
- October 2011
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Background
Although genetic epidemiological studies have confirmed increased rates of major depressive disorder among the relatives of people with bipolar affective disorder, no report has compared the clinical characteristics of depression between these two groups.
AimsTo compare clinical features of depressive episodes across participants with major depressive disorder and bipolar disorder from within bipolar disorder pedigrees, and assess the utility of a recently proposed probabilistic approach to distinguishing bipolar from unipolar depression. A secondary aim was to identify subgroups within the relatives with major depression potentially indicative of ‘genetic’ and ‘sporadic’ subgroups.
MethodPatients with bipolar disorder types 1 and 2 (n = 246) and patients with major depressive disorder from bipolar pedigrees (n = 120) were assessed using the Diagnostic Interview for Genetic Studies. Logistic regression was used to identify distinguishing clinical features and assess the utility of the probabilistic approach. Hierarchical cluster analysis was used to identify subgroups within the major depressive disorder sample.
ResultsBipolar depression was characterised by significantly higher rates of psychomotor retardation, difficulty thinking, early morning awakening, morning worsening and psychotic features. Depending on the threshold employed, the probabilistic approach yielded a positive predictive value ranging from 74% to 82%. Two clusters within the major depressive disorder sample were found, one of which demonstrated features characteristic of bipolar depression, suggesting a possible ‘genetic’ subgroup.
ConclusionsA number of previously identified clinical differences between unipolar and bipolar depression were confirmed among participants from within bipolar disorder pedigrees. Preliminary validation of the probabilistic approach in differentiating between unipolar and bipolar depression is consistent with dimensional distinctions between the two disorders and offers clinical utility in identifying patients who may warrant further assessment for bipolarity. The major depressive disorder clusters potentially reflect genetic and sporadic subgroups which, if replicated independently, might enable an improved phenotypic definition of underlying bipolarity in genetic analyses.