Before you dive into VaR methodologies or option sensitivities, answer this: You need to price a Black-Scholes-Merton (BSM) call option. The stock is $100, strike is $100, time is 1 year, volatility is 20%, and the risk-free rate is 5%. You correctly calculate d1 = 0.35 and d2 = 0.15. Even with perfect math, what single assumption, if violated in the real world, invalidates your result? The trap isn't the formula. It's the model's strict assumption of no dividends. Forgetting to check for or adjust for dividends is a classic pitfall that separates candidates who just memorize from professionals who can actually manage risk.
This FRM Part I Valuation and Risk Models cheat sheet for the 2026 exam distills the 30% weighted domain into essential formulas (VaR, BSM, Duration), key model assumptions, and common traps. It's a focused tool for quick review and reinforcing the concepts most likely to be tested.
Key facts
- Official Body
- Global Association of Risk Professionals (GARP)
- FRM Part I Pass Rate
- Historically 45-50% globally. GARP reports the Part I pass rate typically hovers between 45% and 50% (GARP).
- Study Hours Recommended
- 200-250 hours for Part I.
- Domain Weight
- 30% of the FRM Part I exam (30 questions).
- Exam Format
- 100 multiple-choice questions over 4 hours.
- Key Topics
- VaR, ES, option pricing, fixed income, credit risk, operational risk.
What Does Valuation and Risk Models Cover?
The Valuation and Risk Models section is the quantitative heart of the FRM Part I exam. Accounting for 30 of the 100 questions, it tests your ability to apply mathematical models to value financial instruments and quantify market, credit, and operational risks.
You must be fluent in calculating and interpreting Value-at-Risk (VaR) and Expected Shortfall (ES) using parametric, historical, and Monte Carlo methods. Option pricing using the Black-Scholes-Merton model, along with the practical application of the Greeks (delta, gamma, vega), is a major focus. You'll also face detailed questions on bond valuation, Macaulay and modified duration, convexity, and credit risk metrics like PD, LGD, and EAD.
Studying for FRM Part 1? Benchmark your score in 5 minutes.
Get an instant weak-spot assessment and a custom 12-week study plan PDF generated for your exam window.
Your goal isn't just to memorize formulas. The exam demands you understand the context: the assumptions, the limitations, and the scenarios where one model is superior to another.
What Are the Core Formulas and Frameworks?
Mastering this set of formulas and rules is essential. These are the tools you'll use to solve the majority of quantitative problems in this domain.
Value-at-Risk (VaR) and Expected Shortfall (ES)
VaR quantifies the maximum potential loss over a time horizon at a given confidence level. ES (or CVaR) tells you the expected loss if you breach the VaR threshold.
- Parametric VaR (Normal Distribution): Assumes returns are normally distributed.
🧮 Formula:
VaR = −(μ × Δt + σ × √Δt × Zα)
Where μ is the daily mean, σ is daily volatility, Δt is the time horizon, and Zα is the Z-score for the confidence level (e.g., 1.645 for 95%, 2.33 for 99%). For a portfolio of value P, absolute VaR is P × VaR_return.
- Historical Simulation VaR: Ranks past returns from worst to best. The VaR is simply the loss at the specified percentile (e.g., for a 99% VaR on 1,000 days of data, it's the 10th worst loss). Its main advantage is that it makes no assumptions about the distribution of returns.
- Expected Shortfall (ES): The average of all losses that are greater than or equal to the VaR. It provides a better sense of the tail risk.
Option Pricing (Black-Scholes-Merton)
The BSM model is used to price European options on non-dividend-paying stocks.
- Call Price (C):
C = S × N(d1) − K × e^(−rT) × N(d2) - Put Price (P):
P = K × e^(−rT) × N(−d2) − S × N(−d1) - d1:
[ln(S/K) + (r + (σ^2)/2) × T] / (σ × √T) - d2:
d1 − σ × √T
- Current Stock Price (S) = $105
- Strike Price (K) = $100
- Time to Expiration (T) = 0.5 years
- Risk-Free Rate (r) = 5% (0.05)
- Volatility (σ) = 20% (0.20)
Step 1: Calculate d1
d1 = [ln(105/100) + (0.05 + (0.20^2)/2) × 0.5] / (0.20 × √0.5)
d1 = [0.04879 + (0.07) × 0.5] / (0.14142)
d1 = [0.04879 + 0.035] / 0.14142 ≈ 0.5925
Step 2: Calculate d2
d2 = 0.5925 − 0.20 × √0.5 ≈ 0.4511
Step 3: Find N(d1) and N(d2)
Using a standard normal distribution table:N(0.5925) ≈ 0.7233
N(0.4511) ≈ 0.6740
Step 4: Calculate Call Price (C)
C = 105 × 0.7233 − 100 × e^(−0.05 × 0.5) × 0.6740
C = 75.9465 − 100 × 0.9753 × 0.6740
C = 75.9465 − 65.745 ≈ $10.20Hedging with Option Greeks
The Greeks are not just for pricing; they are essential for hedging.
- Delta (Δ): Change in option price for a $1 change in the underlying's price. A delta-neutral portfolio is hedged against small price moves.
- Gamma (Γ): Change in delta for a $1 change in the underlying's price. Gamma hedging protects against larger price moves by adjusting the hedge as the underlying moves. A portfolio that is delta-neutral but has negative gamma will lose money if the underlying price moves significantly in either direction.
- Vega: Sensitivity to volatility. Vega hedging involves taking positions in other options to neutralize volatility risk.
Bond Valuation, Duration, and Convexity
These are the core tools for managing interest rate risk in fixed-income portfolios.
- Bond Price: The sum of the present values of all future cash flows (coupons and principal).
- Modified Duration: The approximate percentage price change of a bond for a 1% change in its yield. A higher duration means higher interest rate sensitivity.
- Convexity: Measures the curvature in the price-yield relationship. For large yield changes, duration alone is inaccurate. A positive convexity is beneficial, as the bond's price increases more when yields fall than it decreases when yields rise.
Credit Risk Models
Credit risk is measured by quantifying potential losses from a borrower's failure to pay.
- Expected Loss (EL):
EL = PD × LGD × EAD - Probability of Default (PD): The likelihood a borrower defaults.
- Loss Given Default (LGD): The percentage of exposure lost upon default.
- Exposure at Default (EAD): The amount owed at the time of default.
Operational Risk (Finalized Basel III / Basel IV)
The old approaches (BIA, SA, AMA) have been replaced. For the 2026 exam, you must know the new single non-model-based method.
- Standardized Measurement Approach (SMA): This is the current framework for calculating operational risk capital. It uses a formula based on a Business Indicator Component (BIC) and an Internal Loss Multiplier (ILM).
🧮 Formula: OpRisk Capital = BIC × ILM
- The BIC is calculated from a bank's financial statement items (interest, services, trading income).
- The ILM is a scaling factor based on the bank's historical operational loss experience relative to the BIC. An ILM greater than 1 increases the capital requirement, reflecting poor historical loss control.
Calculate Your FRM Part 1 Score & Study Hours by Domain
Adjust your practice scores across official FRM Part 1 blueprint domains to predict your pass probability and generate a domain-weighted study schedule.
What Are the Most Common Exam Traps?
The FRM exam is designed to catch candidates who rely on surface-level knowledge. Here’s where people lose points.
Misinterpreting Model Assumptions
This is the biggest trap. You calculate a perfect BSM price but forget the question mentioned a dividend-paying stock. Or you apply a normal distribution VaR model to a dataset with obvious fat tails.
The wrong answer is tempting because the math feels right.
Always ask: What are the assumptions of this model, and does the question violate any of them?
Unit and Time Inconsistency
A classic error is mixing time units. A question gives you annual volatility but asks for a 10-day VaR. If you forget to scale the volatility (σ_10day = σ_annual × √(10/252)), you will get one of the distractor answers. Double-check that all your inputs (rates, volatility, time) are in consistent units before you calculate.
Confusing VaR and Expected Shortfall
A question might ask for ES but provide all the information to calculate VaR. A candidate in a hurry will calculate the VaR, find it among the answer choices, and move on. Remember, ES is the average loss beyond the VaR point. It will always be a larger loss (a more negative number) than the VaR at the same confidence level.
VoraPrep's adaptive question bank includes thousands of questions with detailed rationales that explain not just the right answer, but also why each distractor is tempting. You can try some free FRM questions here to see how these traps work in practice.
How Can Mnemonics Help on Exam Day?
Mnemonics are shortcuts to recall lists and formulas under pressure. The best ones are those you create yourself, but here are a few to get you started.
- VaR Methods: "HMP" for Historical, Monte Carlo, Parametric.
- Option Greeks: "Don't Get Violent, Things Run" for Delta, Gamma, Vega, Theta, Rho.
- EL Components: "People Lose Everything" for PD, LGD, EAD. (Note: The formula is PD x LGD x EAD, the mnemonic just helps recall the components).
Focus your memorization efforts on core formulas, the specific assumptions of each model, and key definitions that distinguish similar concepts (like VaR vs. ES or Macaulay vs. Modified Duration).
How Should I Use This Cheat Sheet?
A cheat sheet is for reinforcement, not initial learning. Use it strategically.
- Before Practice: Spend five minutes reviewing the relevant formulas here before starting a practice quiz on that topic. This primes your brain.
- After Practice: When you get a question wrong, come back here to review the base formula or concept. Then, read the detailed question explanation in your study platform to understand the nuance you missed.
- Final Weeks: In the last 2-3 weeks before your exam, this sheet should be a daily review tool to keep the most important information fresh.
The most effective study loop is: Review Concept (Cheat Sheet) -> Apply Concept (Practice Questions) -> Analyze Mistakes (Detailed Explanations). VoraPrep's complete course integrates this loop with textbook-grade lessons, FSRS flashcards, and a personalized study plan to guide you.