Rule Atlas
Basel III: Option Valuation: Models, Implied Volatility, and Greeks
Under Basel III (GARP / Basel Committee), option Valuation: Models, Implied Volatility, and Greeks establishes the authoritative rules tested on the GARP FRM® Part I. Explores binomial and Black-Scholes-Merton models for option valuation, the concept of implied volatility, and the practical application of option Greeks. VoraPrep verifies every threshold, worked table, and practice question below against the current GARP FRM® Part I blueprint.
Core Statutory Concepts
| Feature | Binomial Tree Model | Black-Scholes-Merton (BSM) Model |
|---|---|---|
| Time Steps | Discrete | Continuous |
| Option Type | American & European | European only |
| Underlying Asset | Can handle dividend payments and other complexities | Typically for non-dividend-paying stocks |
| Volatility | Assumed constant within each step, but can vary over time | Assumed constant over the option's life |
| Risk-Free Rate | Assumed constant | Assumed constant |
| Methodology | Risk-neutral valuation, iterative back-calculation | Closed-form solution based on Ito's Lemma |
| Complexity | More computationally intensive for many steps | Analytical, but relies on restrictive assumptions |
| Citation | GARP FRM Learning Objectives (Option Valuation) | GARP FRM Learning Objectives (Option Valuation) |
A portfolio manager holds a long position in a call option and has established a delta-neutral hedge. If the underlying stock price subsequently experiences a significant decrease, what action would most likely be required to maintain the delta-neutral position?
Practitioner Application: Option Valuation: Models, Implied Volatility, and Greeks
A portfolio manager is evaluating a European call option and needs to understand its sensitivity to underlying price changes, volatility, and time decay. They must select the appropriate valuation model and interpret its risk metrics to make an informed hedging decision, aligning with GARP FRM Learning Objectives related to option pricing and risk management.
- Option valuation models provide theoretical prices for derivatives, enabling risk managers to assess fair value and associated risks. The binomial tree model and the Black-Scholes-Merton (BSM) model are fundamental approaches, each with distinct assumptions and applications.
- Binomial Tree Model This is a discrete-time model that assumes the underlying asset price can only move to one of two possible prices (up or down) during each period. It uses a risk-neutral valuation approach, meaning the expected return on all assets is the risk-free rate. It's particularly useful for American options where early exercise is possible, as it can be adapted to evaluate early exercise opportunities.
Common GARP FRM® Part I Distractors on Basel III
- 1⚠️ Exam trap: Confusing European and American options when applying models. The BSM model is strictly for European options. While a binomial model can price both, using BSM for an American option that has significant early exercise value will undervalue it.
- 2Binomial vs. BSM: Use binomial for American options and where early exercise or discrete events (e.g., dividends) are relevant. Use BSM for European options on non-dividend-paying assets.
- 3Implied Volatility: It's the market's forward-looking expectation of volatility, derived from an option's market price using a pricing model.
- 4- Delta: Sensitivity to underlying price change (first-order).
- 5- Gamma: Sensitivity of Delta to underlying price change (second-order).
Frequently Asked Questions: Basel III
What is the core rule under Basel III (Option Valuation: Models, Implied Volatility, and Greeks)?
Under Basel III (GARP / Basel Committee), option Valuation: Models, Implied Volatility, and Greeks establishes the authoritative rules tested on the GARP FRM® Part I. Explores binomial and Black-Scholes-Merton models for option valuation, the concept of implied volatility, and the practical application of option Greeks. VoraPrep verifies every threshold, worked table, and practice question below against the current GARP FRM® Part I blueprint.
How is Basel III tested on the GARP FRM® Part I?
⚠️ Exam trap: Confusing European and American options when applying models. The BSM model is strictly for European options. While a binomial model can price both, using BSM for an American option that has significant early exercise value will undervalue it. Binomial vs. BSM: Use binomial for American options and where early exercise or discrete events (e.g., dividends) are relevant. Use BSM for European options on non-dividend-paying assets.
Where can I practice GARP FRM® Part I questions on Option Valuation: Models, Implied Volatility, and Greeks?
Test yourself instantly with the free playable GARP FRM® Part I question on this page, or launch VoraPrep's full GARP FRM® Part I adaptive question bank, interactive lessons, and 1:1 exam simulator at voraprep.com/frm.