In the context of reputation of large corporate organisations, accumulating time series of sentiment values provides an illuminating view of company performance that is not reflected in the balance sheet. Calculating cumulative sentiment enables a risk manager to see 'at a glance' whether the sentiment trend is positive or negative in cases where daily sentiment varies considerably. Using a large data set, a power law and a lookup table are developed so that the sentiment trend of an organisation can be compared with those of other organisations without any knowledge of those others. The resulting decision rule is easy to apply. Its strength lies in its simplicity. Significantly, the linear nature of most cumulative sentiment plots imply that it is very difficult to reverse sentiment direction.

Periodic behaviour of reputation time series is investigated by Fourier series approximations. Harmonics of increasing frequency are successively added to an initial base harmonic until a stop criterion is triggered. The stop condition is determined by formulating a novel ‘sufficient convergence’ criterion based on an error bound when approximating discrete data by a Fourier aeries. The results show that 70

The problem of preserving autocorrelation and volatility characteristics in reputational time series forecasting is approached by Block Bootstrapping. Sentiment time series are tokenised by partitioning them into small blocks, and classifying each block as one of five characteristic shapes. LSTM is used to generate sequences of single tokens, each associated with a small data block. Forecasts are built by concatenating those small data blocks. The generative model is evaluated relative to dedicated autocorrelation and volatility criteria, and is compared with non-generative models in which blocks are selected from the historic data at random. Evaluations based on 130 reputation time series show that the generative model is optimally performant for volatility, up to a range of approximately six months. Success rates are in the range 91–99

Reputations of corporate organisations are valued in monetary terms relative to share capital using an Event Tracking method. Reputational events are first identified from turning points on time series of daily sentiment scores. Sentiment and share prices are then traced after those events. A sentiment projection, derived from a neural network, is then made for the periods immediately following each event. Reputation monetisation is measured by comparing the difference between actual and projected sentiment, compared with the corresponding share price change. The results indicate that reputation accounts for less than 9.6

We present a quantitative definition of reputation risk, formulated in terms of a reputation time series comprising daily sentiment measurements. Self Supported Learning is used to quantify reputation risk by progressively refining an initial proposal for a Minimum Acceptable Sentiment, calculated from descriptive statistics of the reputation data. The derived values are validated using a "sense test" based on a Loess quantile. The results show that the Minimum Acceptable Sentiment value is given approximately by a two standard deviation lower tail of the observed data.

Value-at-risk estimates derived from extreme value data by fitting fat-tailed distributions can be so large that their validity is open to question. In this paper, an objective criterion, and a framework from which it was developed, are presented in order to decide whether or not a fitted distribution is inappropriate for the purpose of value-at-risk calculation. That criterion is based on established extreme value theory (principally the Pickands-Balkema-deHaan Theorem), which is used to calculate a sequence of reference value-at-risk estimates using Generalised Pareto distributions. Those estimates are used to develop a closed-form formula for calculating a theoretical 'maximum' value-at-risk. The method is validated by generating 100 random data sets and testing them against the framework for varying input parameter values. Approximately 75% of those cases passed the validation test.

Regression and machine learning methods are applied to the problem of Value-at-Risk determination in the context of financial Operational Risk, in order to determine an optimal technique that agrees sufficiently well with established Monte Carlo analyses. The annualised sum of operational losses is identified as the most significant statistical influence on Value-at-Risk , and a technique using it as a proxy for measured Value-at-Risk in a Test environment is formalised. The optimal stand-alone model is Generalized Additive, with approximately 61% success. The success rate can be enhanced to approximately 65% using a stacked model.

Some value-at-risk (VaR) calculations yield extremely large results, which are often rejected on the grounds that they are inconsistent with the operational loss profile of the organization concerned. Therefore, an informal limit has effectively been placed on VaR. Hitherto, the concept of a "maximum" VaR has rarely been considered. In this paper, we propose an objective and simple process to determine whether or not a calculated VaR is "too large", and thereby give a precise definition of "too large" in this context. A simple decision process, using a constant multiplier of the annualized sum of losses, is proposed to reject distributions that produce extremely high VaR values. This decision process works in conjunction with a bootstrap to also reject distributions that produce very low VaR values. Together, they determine whether or not a calculated VaR value is "credible". A practical guide to using the combined procedures is given, along with a discussion of potential problems and viable solutions to those problems.

Calculating the amount of regulatory capital to cover unexpected losses due to operational events in the upcoming year has caused problems because of difficulties in fitting probability distributions to data. It is consequently difficult to judge an appropriate level of capital that reflects the risk profile of a financial institution. We provide theoretical and empirical analyses to link the calculated capital to the sum of losses using appropriate statistical approximations. We conclude that, in order to reasonably reflect the associated risk, the capital should be approximately half the sum of losses, with a wide bound for the ratio of capital to sum.

Intuitively, similar customers should have similar credit risk. Capturing this similarity is often attempted using Euclidean distances between customer features and predicting credit default via logistic regression. Here we explore the use of topological data analysis for describing this similarity. In particular, persistent homology algorithms provide summaries of point clouds which relate to their topology. This approach has been shown to be useful in many applications but to the best of our knowledge, applying topological data analysis to prediction of credit risk is novel. We develop a pipeline which is based on the topological analysis of neighbourhoods of customers, with the neighbourhoods determined by a geometric network construction. We find a modest signal using three data sets from the Lending Club, and the Japan Credit Screening data set. The Cleveland oncological data set is used to validate the pipeline. The results have high variance, but they indicate that including such topological features could improve credit risk prediction when used as additional explanatory variable in a logistic regression.

Some Value-at-risk estimates can be so large that their validity is questionable, and are subjectively rejected. An objective rejection criterion, based on a comparison of empirical data with a Generalised Pareto model of the data tail and applying the Pickands-Balkema-deHaan Theorem is presented. A consequent definition and measure of ’Maximum Value-at-risk’ is developed and validated.

Correlations between operational risk loss severity, frequency and economic factors have been used as a de facto tool to assess economic and regulatory capital since 1990. We demonstrate, using data from a single retail bank, that such correlations do not apply universally, and that projections of capital requirements are subject to wide error margins. Some correlations can be explained in terms of data trends. Given worldwide regulatory requirements to assess the resilience of financial institutions to economic shocks, an alternative to using correlations that makes use of economic data is proposed. The proposal is consistent with a much broader interpretation of capital allocation than has applied to date. Evidence that the Covid-19 pandemic had minimal effect on operational risk losses in 2020 is presented and the effect of model risk is emphasized. Our results show that the existence or otherwise of significant correlations depends on the regression model used, whether data series show trends, the time window concerned, geographical location and the type of financial institution.

Previous work has established that the distribution of daily reputation scores is best modelled by a bi-partite pair of exponential distributions. Simulations developed from that distributional model did not account for auto-correlations in the data. We now extend the bi-partite model in two ways. Candidate auto-correlation methods are assessed in order to incorporate the auto-correlation structure of the data in a simulation. Negative reputational shocks are then modelled using a chi-square distribution, so that they can then adequately model runs of successive days of either positive or negative sentiment. Auto-correlation goodness-of-fit tests show that the optimal auto-correlation model uses the fitted auto-regression components of the original data, and that goodness-of-fit can be improved by inflating them by about 1%. This optimised model is successful in at least 88% of simulations where auto-correlation in the original data does not extend beyond 10 lags. In other cases (mainly due to severe reputational shock), 80% success can be expected. Examples of shock simulations for large corporate organisations are shown, and the implications for reputational analysis are discussed.

Selecting a suitable method to solve a black-box optimization problem that uses noisy data was considered. A targeted stop condition for the function to be optimized, implemented as a stochastic algorithm, makes established Bayesian methods inadmissible. A simple modification was proposed and shown to improve optimization the efficiency considerably. The optimization effectiveness was measured in terms of the mean and standard deviation of the number of function evaluations required to achieve the target. Comparisons with alternative methods showed that the modified Bayesian method and binary search were both performant, but in different ways. In a sequence of identical runs, the former had a lower expected value for the number of runs needed to find an optimal value. The latter had a lower standard deviation for the same sequence of runs. Additionally, we suggested a way to find an approximate solution to the same problem using symbolic computation. Faster results could be obtained at the expense of some impaired accuracy and increased memory requirements.

A black-box optimization problem is considered, in which the function to be optimized can only be expressed in terms of a complicated stochastic algorithm that takes a long time to evaluate. The value returned is required to be sufficiently near to a target value, and uses data that has a significant noise component. Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution, and its effectiveness is measured in terms of the number of function evaluations required to attain the target. To improve results, a simple modification of the Gaussian Process ‘Lower Confidence Bound’ (LCB) acquisition function is proposed. The expression used for the confidence bound is squared in order to better comply with the target requirement. With this modification, much improved results compared to random selection methods and to other commonly used acquisition functions are obtained.

Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution to a black-box optimization problem in which the function to be optimized has particular properties that result in difficulties. It can only be expressed in terms of a complicated and lengthy stochastic algorithm, with the added complication that the value returned is only required to be sufficiently near to a pre-determined ‘target’. We consider the context of financial stress testing, for which the data used has a significant noise component. Commonly-used Bayesian Optimization acquisition functions cannot analyze the ‘target’ condition in a satisfactory way, but a simple modification of the ‘Lower Confidence Bound’ acquisition function improves results markedly. A proof that the modified acquisition function is superior to the unmodified version is given.

A model for financial stress testing and stability analysis is presented. Given operational risk loss data within a time window, short-term projections are made using Loess fits to sequences of lognormal parameters. The projections can be scaled by a sequence of risk factors, derived from economic data in response to international regulatory requirements. Historic and projected loss data are combined using a lengthy nonlinear algorithm to calculate a capital reserve for the upcoming year. The model is embedded in a general framework, in which arrays of risk factors can be swapped in and out to assess their effect on the projected losses. Risk factor scaling is varied to assess the resilience and stability of financial institutions to economic shock. Symbolic analysis of projected losses shows that they are well-conditioned with respect to risk factors. Specific reference is made to the effect of the 2020 COVID-19 pandemic. For a 1-year projection, the framework indicates a requirement for an increase in regulatory capital of approximately 3% for mild stress, 8% for moderate stress, and 32% for extreme stress. The proposed framework is significant because it is the first formal methodology to link financial risk with economic factors in an objective way without recourse to correlations.

Recent high profile breaches of regulation by prominent UK financial institutions suggest that self-regulation is ineffective. Intuitively, regulatory breaches should result in a tarnished reputation, but that conjecture is unsubstantiated. With objective measurement of reputation, we demonstrate that reputational damage is not a significant deterrent against regulatory breaches. Imposing regulatory fines is also no deterrent. We speculate that customers are prepared to tolerate large regulatory breaches: retail customers provided they are not affected personally, and corporate customers as long as investments do not devalue. Regulation has not previously been linked to reputation, and this result is significant because it adds to the argument that external regulation remains necessary. Note is also made of recent unsuccessful initiatives on self-regulation.

Analysing credit data using a neural network has hitherto proved to be very resilient to attempts to improve success rates in prediction. We present a technique using simulated data which results in a marginal improvement in success rate. The empirical probability distribution for each feature of the training data is determined, and random samples are drawn from those distributions. The result is termed ‘artificial’ data. It is then possible to generate equal volumes of data for each of the binary outcomes (default or not), thereby alleviating a class imbalance classification problem. The simulation method uses a copula (to preserve the correlation structure of the original data) and optimal feature weighting to give acceptable results. The results indicate that overall percentage success rates for the more common outcome only are improved, but there is a more significant improvement in the AUC metric. The significance of this result in the context of assessing credit worthiness is discussed.

Poor performance of artificial neural nets when applied to credit-related classification problems is investigated and contrasted with logistic regression classification. We propose that artificial neural nets are less successful because of the inherent structure of credit data rather than any particular aspect of the neural net structure. Three metrics are developed to rationalise the result with such data. The metrics exploit the distributional properties of the data to rationalise neural net results. They are used in conjunction with a variant of an established concentration measure that differentiates between class characteristics. The results are contrasted with those obtained using random data, and are compared with results obtained using logistic regression. We find, in general agreement with previous studies, that logistic regressions out-perform neural nets in the majority of cases. An approximate decision criterion is developed in order to explain adverse results.