Operational Risk Modeling and Lognormal Distribution
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Questions and Answers

What characteristic of operational risk scenarios influences the choice of distribution for modeling?

  • Normal distribution properties
  • Heavy-tailed nature (correct)
  • Uniformly distributed risks
  • Predictable outcomes

Which property of the Lognormal distribution makes it particularly suitable for operational risk modeling?

  • It requires complex calibration methods.
  • It is a sub-exponential distribution. (correct)
  • It has infinite parameters for flexibility.
  • It is valid only in non-financial sectors.

What is a primary reason for using the Lognormal distribution in banking regulation compliance?

  • It generates standard deviations.
  • It limits parameter variability.
  • It requires many parameters to understand the risks.
  • It complies with sub-exponential distribution requirements. (correct)

What is the maximum number of parameters required for calibrating the Lognormal distribution?

<p>Two (A)</p> Signup and view all the answers

Which of the following describes a limitation of using other distributions compared to the Lognormal for operational risk modeling?

<p>Higher complexity in understanding parameters. (A), More constraints on parameter choices. (C), Lower compliance with banking regulations. (D)</p> Signup and view all the answers

What does the Advanced Measurement Approach (AMA) primarily focus on for quantifying Operational Risk?

<p>Frequency and severity of loss events (C)</p> Signup and view all the answers

In the context of operational loss, what does $X_i$ represent in the aggregate loss formula?

<p>The loss of a single event (B)</p> Signup and view all the answers

What is assumed about the claims when applying the Advanced Measurement Approach?

<p>Claims are independent and identically distributed (A)</p> Signup and view all the answers

How is risk-capital calculated under Solvency II principles?

<p>By aggregating loss distributions with a Value-at-Risk approach (D)</p> Signup and view all the answers

What statistical method is commonly used to combine frequency and severity in operational risk analysis?

<p>Monte Carlo simulations (B)</p> Signup and view all the answers

What is typically the time frame for quantifying the distribution of frequency in loss events?

<p>One year (B)</p> Signup and view all the answers

What does the formula for aggregate loss represent?

<p>Sum of individual losses from multiple events (B)</p> Signup and view all the answers

What characteristic of claims is considered when analyzing operational risk within risk management frameworks?

<p>There is independence between the number of claims and their magnitude (C)</p> Signup and view all the answers

What does the variable $p_{W C}$ represent in the context provided?

<p>The percentile of the worst case event (B)</p> Signup and view all the answers

How is the shape parameter $σ$ determined according to the model?

<p>It is chosen by an expert team. (D)</p> Signup and view all the answers

What does the equation $µ=ln(y_0)-σϕ−1(p_{W C})$ calculate?

<p>The parameter of the distribution (D)</p> Signup and view all the answers

What does Monte Carlo simulation help analyze in cyber risk scenarios?

<p>Possible threat outcomes and potential losses at various probability levels (C)</p> Signup and view all the answers

In the worst case risk assessment, how often is the loss expected to occur?

<p>Once every 20 years (D)</p> Signup and view all the answers

What is implied by 'frequency' in the context of risk assessment models?

<p>The average occurrence of all events in the assessed scenario (B)</p> Signup and view all the answers

What aspect of the model is crucial for understanding cyber risks effectively?

<p>Simulation of possible threat outcomes (A)</p> Signup and view all the answers

Which of the following best describes the goal of the cyber risk model architecture presented?

<p>To address and quantify cyber risks through simulations (D)</p> Signup and view all the answers

Flashcards

Operational Risk Quantification

Using models, like the Advanced Measurement Approach (AMA), to estimate operational risk losses by combining frequency and severity of events.

Frequency in Operational Risk

The number of loss events in a specific period, often a year. It is a key factor in estimating operational risk.

Severity in Operational Risk

The magnitude, or size, of a single loss event in operational risk.

Advanced Measurement Approach (AMA)

A method for quantifying operational risk, using Frequency and Severity, especially for insurance companies.

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Aggregate Loss

The total loss amount incurred in a specific period from operational risk events.

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Monte Carlo approach

A simulation technique used to generate the probability distributions of losses in Operational Risk.

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Value-at-Risk (VaR)

A statistical risk measure used to calculate the potential loss for a given confidence level, such as 99.5%.

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Risk Capital

The capital required to cover potential losses from risk exposure.

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Why is Lognormal used for Operational Risk?

The Lognormal distribution is widely used for modeling operational risk severity because it exhibits heavy tails, requires minimal data for calibration, has transparent parameters, complies with banking regulations, and is practical with flexible parameter choices. It's also the industry benchmark.

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What are the three points for Lognormal calibration?

The first approach to calibrating a Lognormal distribution uses three points: the typical impact, the 99.5% percentile, and the 99.9% percentile. These points represent different levels of risk exposure.

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What are typical impact, 99.5% percentile, and 99.9% percentile?

The typical impact represents the most likely loss, 99.5% percentile is the loss exceeded 0.5% of the time, and 99.9% percentile is the loss exceeded 0.1% of the time. These points help to define the shape of the Lognormal distribution.

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How do these three points help calibrate the Lognormal distribution?

By specifying the three points (typical impact, 99.5% percentile, 99.9% percentile), you can estimate the parameters (µ and σ) of the Lognormal distribution. These parameters then define the complete distribution.

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What are the parameters of the Lognormal distribution?

The Lognormal distribution has two parameters: µ and σ. µ is the mean of the logarithm of the random variable, and σ is the standard deviation of the logarithm of the random variable. These parameters determine the shape and location of the distribution.

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Worst Case Event

An event that occurs once every 20 years, representing the highest possible loss in a given scenario.

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Percentile of Worst Case Event (pWC)

The probability of the worst case event occurring, calculated as 1 - (1 / (20 * f)), where 'f' is the average frequency of events.

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Shape Parameter (σ)

A value chosen by experts to determine the spread of the loss distribution, reflecting the uncertainty of possible outcomes.

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Amount of Worst Case Event (y0)

The financial value of the loss associated with the worst case event.

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Cumulative Function of a Standard Gaussian (ϕ())

A mathematical function that calculates the probability of a random variable being less than a specific value in a standard Gaussian distribution.

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Cyber Risk Quantification

The process of measuring and estimating the financial impact of cyber threats, using models and simulations.

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Monte Carlo Simulation

A technique that uses random sampling to simulate possible threat outcomes, generating a range of potential losses.

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Expected and Unexpected Loss

The Monte Carlo simulation returns both the average expected loss and the potential for unexpected losses at different probability levels.

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Study Notes

Graduate Management School

  • POLIMI Graduate Management School
  • International master in financial risk management (İMİFRİM)

Digital Risk Management in the Insurance Sector

  • Digital risk management in the insurance sector is presented at the POLIMI Graduate Management School
  • Valeria Scacco, Partner, Actuarial Services- PwC, presented the topic
  • The presentation covered the role of risk management, governance, non-financial risk, and the Insurer's stance on non-financial risk.
    • Including digital/cyber risk

Agenda

  • Digital risk management in the insurance sector
  • Governance in the regulatory context - Pillar I: general principles and standard formula; Pillar II: process overview, ORSA process
  • Non-financial risks (approaches and the role of risk management): Operational risk and digital risk methodologies for measurement
  • Scenario-based approach (SBA) for operational risk (digital)
  • Procedure for identification, selection, analysis, and aggregation
  • The insurer's stance on non-financial risks including digital risk: cyber risk
    • Definition
    • Impact
  • Cyber risk scenarios; modelling, and insurance coverage -Interactive demo

Speaker

  • Valerio Scacco (Partner-Actuarial Services, PwC)
  • Actuary, PhD
  • Multiple years of experience in risk management in the insurance sector. -Modeling of solvency capital requirements in the Solvency II framework
  • Participation in implementation and validation projects in operational risk.

Solvency I and II

  • Solvency I: had limitations in relation to risk management, capital requirements based on technical factors
  • Solvency II: Defines a new regime; emphasis on risk management and internal controls, places greater emphasis on the quality of risk management and soundness of internal controls, based on principles instead of rules
  • Defines capital requirements as a result of forward-looking valuation. Takes into account financial, technical, counterparty and operational risks -Introduces a joint risk management approach for assets, liabilities. Consists of three pillars:
  • Pillar I (SCR)
  • Pillar 2 (ORSA)
  • Pillar 3 (QRTs). Risk Management is part of Pillar 2

Regulatory Context

  • First-level measures: Solvency II Directive, Omnibus II Directive
  • Second-level measures: Delegated Acts, amendments to delegated acts, first sets of ITS
  • Third-level measures: First and second sets of guidelines -IVASS regulations, Review of regulations, and letters to the market

SII - Pillar I: General Principles

  • Assets and Liabilities are valued at fair market values
  • Technical reserves correspond to the current amount insurance companies would have to pay if they immediately transferred insurance obligations
  • Methods for valuing include Mark to Market and Mark to Model approaches

SII - Pillar I: Standard Formula

  • Methods for calculating SCR including scenario testing approach (SA) and Factor-based approach (FBA)
  • Modules and submodules (Market, Health, Default, Life, Non-life, Intangible) for Risk assessment including loss distribution and analysis
  • Modules include: Market Risk, Credit Risk, Underwriting Risk (Non-Life, Life, Health), and Operational Risk.

SII - Pillar II: ORSA Process and Policy

  • ORSA policy: Policies for assessment of current and future risks and solvency, evidence for risk assessments, internal reports, and ORSA reporting to the Supervisory Authority
  • Risk measurement processes and procedures used for ORSA
  • Risk profile of the company, approved risk tolerance levels, and the total solvency requirement
  • Frequency of qualitative analyses( stress tests, sensitivity analyses, reverse stress) and data quality standards
  • Minimum contents for ORSA Report including risk profile, explanation of current and forward-looking assessments, and linking assessment results to other capital management strategies

SII - Pillar II: ORSA Policy Structure

  • Introduction, Risk Governance, Risk Management System, Current & Forward-looking assessment, Stress Test and Scenario Analysis, ORSA and Capital Allocation, ORSA Report
  • Processes and procedures for ORSA, link between risk profile and approved risk tolerances, qualitative and quantitative analyses, and data quality

SII - Pillar II: ORSA Report

  • Company risk profile and strategy
  • Explanation of current and forward-looking assessments including time horizon of 3+ years, data type and quality, and assessment results
  • Detailed illustration of conclusions drawn from assessment and related actions; including connections to capital management and business planning
  • Additional elements (Contingency plans, management actions), linking to Standard Formula (Adequacy)

Pillar I vs Pillar II

  • Methods for calculating capital requirements; Standard Formula (Pillar I) for individual risk modules, ORSA (Pillar II) for assessing all risks, quantitative/qualitative risk assessment, probability levels, considering the firm's risk profile

SII - Pillar II: Risks Not Included in Pillar I

  • Liquidity risk
  • Group risk
  • Reputational risk
  • Climate risk

Non-financial risks - Operational Risk (Digital Risk)

  • Operational risk
    • Arises from failures of internal processes, human resources, systems, or from external events
  • Digital risks
    • Often associated with operational risks
  • Methods for quantification, calibration, and modeling operational risk, including the Standard Formula Approach -Capital Requirement for operational risks is equal to min (0.3BSCR; Op) + 0.25 Expul

Non-financial risks - Digital and Operational Risks

  • Methods for modeling and calibrating severity and frequency distributions, including loss data approach (LDA), scenario-based approach (SBA), use
  • of lognormal distributions

Model Output

  • Output tables and graphs for each scenario
  • Visualization with risk intelligence tools
  • Loss probability and aggregate exposure distributions that take into consideration risk dependencies
  • Allocate overall risk exposure using model blocks as risk source intelligence tools

Cyber Risk

  • Definition: Risk arising from electronic data use, transmission, technology tools, and cybersecurity incidents

  • Cyber risk is considered as external fraud within risk-types

  • Cyber risks considerations and exposures -Focus on IoT, cloud, and IT

  • Coverage for cyber risks in different sectors (Finance, Public Sector, Wholesale & Retail, etc.)

  • Key findings of a survey of PwC

  • Qualitative & Quantitative factors considered in pricing cyber-covers

  • Silent/non-affirmative risks

  • Case study / interactive demo

Thank You

  • Contact Information
  • Legal Notes

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Description

This quiz explores the characteristics of operational risk scenarios and the application of the Lognormal distribution in modeling. Key topics include the use of the Advanced Measurement Approach (AMA) and principles under Solvency II for quantifying operational risk. Test your understanding of these concepts in the context of banking regulation compliance.

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