Derivative Pricing and Models
How do you price something that derives its value from something else? These articles explore the models behind derivative pricing — from Black-Scholes and binomial trees to Monte Carlo simulation. Understanding pricing theory helps you evaluate whether a derivative is fairly valued and why markets sometimes get it wrong.
No-Arbitrage Principles in Derivatives
Learn how replication and funding mechanics enforce no-arbitrage across futures, options, and swaps, including tolerance bands and mispricing controls.
Binomial Trees for Option Pricing
Learn how binomial trees price options through recombining nodes, backward induction, and early exercise checks, with practical delta and gamma extraction.
Backtesting Pricing Models Against Market Data
Every pricing model is wrong. The question is whether yours is wrong in ways that cost you money. Backtesting—replaying historical market conditions through your model and measuring what it predicted versus what actually happened—is the only systematic way to answer that question. Yet most backte...
Model Risk Governance Practices
Define controls, inventory management, escalation procedures, and audit readiness for derivative pricing models under regulatory requirements.
Open-Source Tools for Derivative Pricing
Evaluate open-source libraries for derivative pricing, including QuantLib, finmath, and best practices for safe integration and maintenance.
Put-Call Parity Applications
Learn how to apply put-call parity for synthetic hedges and arbitrage detection, including dividend adjustments, borrow costs, and desk workflows.
Finite Difference Methods Overview
Learn explicit, implicit, and Crank-Nicolson finite difference schemes for option pricing PDEs, including stability criteria and implementation guidance.
Model Calibration and Validation
Learn calibration and validation workflows for derivative pricing models, including objective functions, overfitting detection, and governance requirements.
Stress Testing Models for Extreme Moves
Learn how to design and execute stress scenarios for pricing models, including scenario libraries, P/L attribution, and remediation governance.
Interest Rate Model Families
Compare short-rate, HJM, and market models for interest rate derivatives, including dynamics, calibration, and deployment considerations.
Pricing Dividend-Paying Underlyings
Learn how discrete and continuous dividends enter option pricing models, including forward adjustments, early exercise considerations, and hedge implications.
Glossary: Derivative Pricing Terminology
A comprehensive reference glossary of derivative pricing terms, including option pricing concepts, volatility measures, Greeks, and model terminology.
Volatility Term Structure Modeling
Learn how volatility term structure connects near-term events to long-term regimes, including modeling techniques and calendar spread implications.
American Option Pricing Approaches
American options require solving a free-boundary problem where the holder can exercise at any moment before expiration. This guide compares binomial trees, finite difference methods, and Longstaff-Schwartz Monte Carlo with production parameters, covers the state-of-the-art Andersen-Lake-Offengenden method (100,000 prices/sec), and includes validation checks and neural network frontiers.
Estimating Greeks Numerically
Learn bump-and-revalue, pathwise, likelihood ratio, and adjoint methods for computing option sensitivities, including step sizes and noise controls.
Black-Scholes Model Inputs and Outputs
Understand Black-Scholes model inputs, calibration workflow, and Greek interpretation for practical options analysis and risk management.
Monte Carlo Simulation Techniques
Learn Monte Carlo methods for derivative pricing, including RNG selection, variance reduction, path-dependent payoffs, and convergence diagnostics.
Local vs. Stochastic Volatility Models
Compare Dupire local volatility, Heston, and SABR stochastic volatility models for exotic option pricing, including calibration and hedge behavior differences.
Implied Volatility Surface Basics
Learn how implied volatility surfaces are built and used, including smiles, skews, term structures, and practical applications for trading and risk.
Smile and Skew Interpretation
Learn to read volatility smiles and skews as sentiment indicators, understand equity vs. FX patterns, and translate signals into hedge adjustments.