Option Greeks, Credit Risk and Liquidity Risk

This document contains the lecture notes converted into flashcards with question and answer format.

Option Greeks

Greeks measure how sensitive the option price is to changes in different market variables.

Delta (Δ)

Measures how much the option value changes for a small change in the underlying price.

Gamma (Γ)

Measures the rate of change of delta with respect to the underlying price.

Vega (ν)

Measures sensitivity of option value to changes in implied volatility.

Theta (Θ)

Measures time decay of option value.

Rho (ρ)

Sensitivity of option value to interest rate changes.

Credit Risk

The possibility that a borrower or counterparty will fail to meet their financial obligations.

Default Risk (Obligor Risk)

Risk that the borrower will fail to repay part or all of the debt (principal + interest).

Downgrade Risk (Migration Risk)

Occurs when a borrower’s credit rating is lowered (e.g., from A to BBB).

Counterparty Credit Risk (CCR)

Applies primarily to derivatives, securities financing transactions, and repos. It is the risk that the counterparty to a financial contract will default before the final settlement.

Lending Credit Risk

Arises in traditional lending: loans, credit cards, mortgages, trade finance, etc.

Probability of Default (PD)

The likelihood that a borrower will default on their obligation within a specified time horizon (usually 1 year).

Loss Given Default (LGD)

Represents the portion of the exposure that is lost if the borrower defaults, calculated as: LGD = (1 − Recovery Rate).

Exposure at Default (EAD)

The total value that the lender is exposed to at the moment of borrower default.

Expected Loss (EL)

The average credit loss anticipated over a given time horizon. Formula: EL = PD × LGD × EAD

Unexpected Loss (UL)

The potential loss exceeding the expected loss, under adverse but plausible scenarios.

Credit Origination

The starting point of any credit relationship between lender and borrower, involving soliciting, receiving, and processing applications for credit products.

Risk Assessment and Underwriting

Focused on evaluating the creditworthiness of the borrower before approval, using quantitative and qualitative factors.

Credit Monitoring and Limit Setting

Once the credit is approved and disbursed, ongoing monitoring is essential to detect deterioration early.

Collections and Recovery

Initiated when a borrower misses payments or enters delinquency stages; involves collection strategies and recovery processes.

Credit Risk

Arises when a borrower or counterparty fails to fulfill contractual obligations, resulting in financial loss, measured using metrics like Probability of Default (PD), Loss Given Default (LGD), etc.

Market Risk

Refers to potential losses due to fluctuations in market variables (interest rates, equity prices, exchange rates, commodity prices), typically more volatile and requires daily VaR monitoring.

Operational Risk

Arises from internal process failures, human error, system failures, or external events; harder to quantify and often managed through risk controls and incident monitoring.

Internal rating systems

Assign credit scores or grades to borrowers based on their risk profile, mapping to default probabilities.

Expert Judgment Models

Rely on qualitative assessments by credit officers and committees, using structured scorecards with defined criteria.

Statistical Models

Use historical data and quantitative methods to predict PD, with common inputs including financial ratios, payment history, and macroeconomic indicators.

Basel II & Basel III Credit Risk Components

International banking regulations providing guidelines for capital adequacy and risk measurement.

Standardized Approach

Uses external credit ratings to assign risk weights to exposures; simpler and more transparent but less risk-sensitive.

Internal Ratings-Based (IRB) Approach

Banks use their own internal credit rating systems to estimate PD, LGD, EAD.

Altman Z-Score

A quantitative credit risk model developed by Edward Altman in 1968 to predict the likelihood of bankruptcy for a firm using accounting-based financial ratios.

Z’-Score (Altman, 1993)

Adapted for private firms by replacing market equity with book equity; omits the market value ratio.

Z’’-Score

Further modified for non-manufacturing and emerging markets; eliminates the sales-to-assets ratio.

Zmijewski Model (1984)

Uses a probit regression model based on three variables: Return on Assets (ROA), Leverage, and Liquidity.

Campbell-Hilscher-Szilagyi (CHS) Model

A modern accounting-based model that includes Net income volatility, Excess return volatility, and Market-to-book ratio.

Merton (Structural) Model

A structural model for credit risk introduced by Robert Merton in 1974, which models a firm’s equity as a European call option on its assets.

External Ratings

Provided by credit rating agencies such as Moody’s, S&P, Fitch, reflecting the agency’s view of creditworthiness based on publicly available and proprietary information.

Internal Ratings

Developed by banks or financial institutions for internal risk management, tailored to the institution’s portfolio and risk tolerance.

Transition Matrix

Shows the probability of migrating from one credit rating to another over a specific time period (usually 1 year).

Probability of Default (PD)

Refers to the likelihood that a borrower will fail to meet their debt obligations within a specified time horizon (usually 12 months).

Logistic Regression in Credit Risk

A statistical method used to model binary outcomes like default, estimating the log-odds of default based on input variables (predictors).

Operational Risk

The risk of loss resulting from inadequate or failed internal processes, people, systems, or external events.

Internal Fraud

Theft, embezzlement, intentional misreporting by employees.

External Fraud

Theft, hacking, robbery, forgery by outsiders.

Employment Practices & Workplace Safety

Discrimination, harassment, workplace injury.

Clients, Products & Business Practices

Mis-selling, product defects, fiduciary breaches.

Damage to Physical Assets

Natural disasters, terrorism.

Business Disruption & System Failures

IT failures, telecom outages.

Execution, Delivery & Process Management

Processing errors, settlement failures.

Frequency and Severity Modeling

Estimates the distribution of future operational losses by separately modeling the number of loss events and the financial impact of each event.

Poisson Distribution

Assumes events are independent and occur with a constant average rate, suitable for low-frequency, random loss events.

Negative Binomial Distribution

Used when variance in loss frequency exceeds the mean, more flexible than Poisson.

Lognormal Distribution

Right-skewed distribution where losses can never be negative, captures multiplicative effects in losses.

Gamma Distribution

Flexible shape that can model both light and moderately heavy tails, often used for legal costs, process errors, or mid-range operational losses.

Generalized Pareto Distribution (GPD)

Modeling extreme or catastrophic operational losses exceeding a high threshold.

Loss Distribution Approach (LDA)

Annual operational risk loss that models losses as a product of event Frequency and the Severity or financial loss per event

Monte Carlo Simulation

A numerical approximation is used to produce a forward-looking approach to quantify annual operational risk loss and used in AMA framework

Credit VaR

Estimates the unexpected loss a credit portfolio may suffer over a given time horizon at a specified confidence level.

Basel Framework

To strengthen risk management, ensure capital adequacy, and promote financial system stability.

Liquidity Coverage Ratio (LCR)

Banks must hold High-Quality Liquid Assets (HQLA) to cover 30-day net cash outflows.

Net Stable Funding Ratio (NSFR)

Ensures banks have sustainable funding over a 1-year horizon

Advanced Measurement Approach (AMA)

Guiding principles banks must ensure they are following to be operating at an acceptable level of risk, liquidity, solvency

Liquidity Risk

The risk that a financial institution cannot meet its obligations when they come due.

Funding Liquidity Risk

Difficulty in obtaining funding to meet short-term needs.

Market Liquidity Risk

Inability to sell assets quickly without price concessions.

Contingent Liquidity Risk

Arises from off-balance sheet commitments (e.g., credit lines, guarantees).

Liquidity Coverage Ratio (LCR)

Ensures banks hold high-quality liquid assets (HQLA) to cover 30-day net outflows.

Net Stable Funding Ratio (NSFR)

Measures long-term funding stability relative to asset profiles over a 1-year horizon.

Liquidity-at-Risk (LaR)

Quantifies potential liquidity shortfall using probabilistic simulations.

Survival Horizon

Time until a firm exhausts liquidity under stressed cash flow conditions.

Idiosyncratic Stress

Bank-specific issues like reputational events or credit downgrades.

Market-Wide Stress

Broad liquidity freeze due to macro shocks or financial crises.

Combined Stress

Simultaneous internal and systemic shocks—used in regulatory stress tests.

Behavioral Assumptions

Captures non-contractual customer behavior, especially in stress, such as early withdrawals of deposits and prepayment of loans etc.

High-Quality Liquid Assets (HQLA)

HQLA are assets that can be easily and immediately converted into cash with little or no loss of value, classify in 3 categories

Liquidity Gap Analysis

Measures mismatch between inflows and outflows across various time buckets, providing visibility into timing mismatches in cash positions.

Liquidity-at-Risk (LaR)

LaR estimates the maximum expected liquidity shortfall over a defined horizon with a confidence level.

Concentration Risk

Large portion of funding depends number of sources, counterparties, or instruments

Early Warning Indicators (EWIs)

Identify emerging liquidity strains before a crisis unfolds and incorporate forward-looking metrics based on market signals and behavioral trends.