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?

Two 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?

Higher complexity in understanding parameters. Signup and view all the answers

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

Frequency and severity of loss events Signup and view all the answers

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

The loss of a single event Signup and view all the answers

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

Claims are independent and identically distributed Signup and view all the answers

How is risk-capital calculated under Solvency II principles?

By aggregating loss distributions with a Value-at-Risk approach Signup and view all the answers

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

Monte Carlo simulations Signup and view all the answers

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

One year Signup and view all the answers

What does the formula for aggregate loss represent?

Sum of individual losses from multiple events Signup and view all the answers

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

There is independence between the number of claims and their magnitude Signup and view all the answers

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

The percentile of the worst case event Signup and view all the answers

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

It is chosen by an expert team. Signup and view all the answers

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

The parameter of the distribution Signup and view all the answers

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

Possible threat outcomes and potential losses at various probability levels Signup and view all the answers

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

Once every 20 years Signup and view all the answers

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

The average occurrence of all events in the assessed scenario Signup and view all the answers

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

Simulation of possible threat outcomes Signup and view all the answers

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

To address and quantify cyber risks through simulations Signup and view all the answers

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.