Derivatives
Educational articles about derivatives.
Subcategories
Options Fundamentals
20 articles
Options Strategies and Greeks
20 articles
Futures and Forwards
20 articles
Swaps and OTC Derivatives
20 articles
Derivative Pricing and Models
20 articles
Volatility and Exotic Products
20 articles
Risk Management and Hedging
20 articles
Operational and Regulatory Considerations
20 articles
Articles
Volatility Surface Construction Techniques
# Volatility Surface Construction Techniques The implied volatility surface maps option prices across strikes and maturities into a coherent fram...
Volatility Futures and Options (VIX) Overview
# Volatility Futures and Options (VIX) Overview VIX futures and options allow investors to trade market volatility directly, rather than indirect...
Variance and Volatility Swap Mechanics
# Variance and Volatility Swap Mechanics Variance swaps and volatility swaps provide pure exposure to realized volatility without the directional...
Valuing Exotics with Monte Carlo Methods
# Valuing Exotics with Monte Carlo Methods Monte Carlo simulation prices derivatives by simulating thousands of possible price paths, calculating...
Tail Risk Hedging with Exotics
# Tail Risk Hedging with Exotics Exotic options can provide more cost-effective tail risk protection than vanilla puts by tailoring payoffs to sp...
Structured Notes Linked to Equity Baskets
# Structured Notes Linked to Equity Baskets Basket-linked structured notes provide exposure to multiple underlying assets within a single investm...
Regulatory Considerations for Structured Products
# Regulatory Considerations for Structured Products Structured products face a complex regulatory landscape spanning securities law, derivatives ...
Managing Volatility Premium Selling Strategies
# Managing Volatility Premium Selling Strategies Volatility premium selling harvests the difference between implied volatility (what options cost...
Hedging Complex Payoffs in Practice
# Hedging Complex Payoffs in Practice Hedging exotic options requires dynamic management of multiple risk factors, often with instruments that do...
Glossary: Exotic and Volatility Products
# Glossary: Exotic and Volatility Products This glossary provides definitions for key terms used in exotic options, volatility products, and stru...
Distribution Practices for Retail Note Offerings
# Distribution Practices for Retail Note Offerings Structured notes reach retail investors through a distribution network involving issuers, dist...
Dispersion Trades Using Options
# Dispersion Trades Using Options Dispersion trading exploits the relationship between index option volatility and single-stock option volatility...
Digital and Binary Options Explained
# Digital and Binary Options Explained Digital options (also called binary options) provide a fixed payoff if the underlying asset finishes above...
Correlation Trading and Basket Options
# Correlation Trading and Basket Options Correlation trading involves taking positions that profit from changes in how assets move together. Bask...
Convertible Bonds as Embedded Options
# Convertible Bonds as Embedded Options Convertible bonds combine debt characteristics with an embedded option to convert into equity at a predet...
Chooser and Compound Options
# Chooser and Compound Options Chooser options and compound options add an additional layer of optionality to standard options. Chooser options a...
Case Studies of Exotic Product Blowups
# Case Studies of Exotic Product Blowups Exotic derivatives have been involved in some of the largest trading losses in financial history. These ...
Barrier Options: Knock-In and Knock-Out Structures
# Barrier Options: Knock-In and Knock-Out Structures Barrier options are path-dependent derivatives whose existence or payoff depends on whether ...
Auto-Callable Notes and Yield Enhancers
# Auto-Callable Notes and Yield Enhancers Auto-callable notes are structured products that pay enhanced coupons and may redeem early if the under...
Asian and Lookback Option Structures
# Asian and Lookback Option Structures Asian options and lookback options are path-dependent derivatives whose payoffs depend on the price histor...
Valuation Adjustments: CVA, DVA, FVA
# Valuation Adjustments: CVA, DVA, FVA Valuation adjustments (XVAs) modify derivative fair values to reflect counterparty credit risk and funding...
Total Return Swaps for Equity Exposure
# Total Return Swaps for Equity Exposure A total return swap (TRS) transfers the total economic performance of a reference asset—including price ...
Terminating or Novating Swap Positions
# Terminating or Novating Swap Positions Swap positions can be closed through termination (mutual agreement to end the trade) or novation (transf...
Swap Execution Facilities (SEFs)
# Swap Execution Facilities (SEFs) Swap Execution Facilities (SEFs) are CFTC-regulated trading platforms for over-the-counter derivatives. Create...
Setting Up Hedge Documentation
# Setting Up Hedge Documentation Proper hedge documentation ensures legal enforceability, enables hedge accounting, and establishes operational c...
Plain-Vanilla Interest Rate Swaps Mechanics
# Plain-Vanilla Interest Rate Swaps Mechanics A plain-vanilla interest rate swap is an agreement between two parties to exchange fixed-rate inter...
ISDA Master Agreement Overview
# ISDA Master Agreement Overview The ISDA Master Agreement is the foundational legal document for over-the-counter derivatives transactions. Publ...
Initial Margin vs. Variation Margin in OTC Trades
# Initial Margin vs. Variation Margin in OTC Trades Initial margin (IM) and variation margin (VM) serve different purposes in managing counterpar...
Hedging Fixed Income Portfolios with Swaps
# Hedging Fixed Income Portfolios with Swaps Interest rate swaps are the primary tool for managing duration and curve exposure in fixed income po...
Glossary: Swap Market Terms
# Glossary: Swap Market Terms This glossary provides concise definitions of swap market terms used throughout the Swaps and OTC Derivatives serie...
Equity Swap Use Cases for Hedge Funds
# Equity Swap Use Cases for Hedge Funds Equity swaps provide hedge funds with flexible, capital-efficient exposure to stocks and indices. Beyond ...
Dodd-Frank and EMIR Reporting Requirements
# Dodd-Frank and EMIR Reporting Requirements Dodd-Frank (US) and EMIR (EU) require comprehensive reporting of OTC derivatives to trade repositori...
Cross-Currency Swaps and Basis Risk
# Cross-Currency Swaps and Basis Risk A cross-currency swap exchanges both principal and interest payments in one currency for principal and inte...
Credit Support Annex and Collateral Terms
# Credit Support Annex and Collateral Terms The Credit Support Annex (CSA) is an annex to the ISDA Master Agreement that governs collateral excha...
Credit Default Swaps Contracts
# Credit Default Swaps Contracts A credit default swap (CDS) is a derivative contract that transfers credit risk from a protection buyer to a pro...
Counterparty Risk Monitoring
# Counterparty Risk Monitoring Counterparty risk monitoring tracks credit exposure to OTC derivatives counterparties, identifies deteriorating cr...
Compression and Portfolio Tear-Ups
# Compression and Portfolio Tear-Ups Compression and tear-up services reduce the gross notional outstanding of OTC derivatives portfolios by term...
Commodity Swaps for Producers and Consumers
# Commodity Swaps for Producers and Consumers Commodity swaps allow producers and consumers to exchange floating commodity prices for fixed price...
Cleared vs. Bilateral Swap Structures
# Cleared vs. Bilateral Swap Structures Cleared swaps use a central counterparty (CCP) to guarantee performance, while bilateral swaps remain dir...
Accounting Treatment for Hedging Swaps
# Accounting Treatment for Hedging Swaps Hedge accounting allows derivatives gains and losses to be matched with the hedged item in the income st...
Vega Hedging for Volatility Surfaces
# Vega Hedging for Volatility Surfaces Vega hedging manages exposure to implied volatility changes across the entire volatility surface—not just ...
Using Options to Hedge Equity Portfolios
# Using Options to Hedge Equity Portfolios Options provide flexible tools for protecting equity portfolios against market declines. Put options e...
Using Futures to Hedge Commodity Exposure
# Using Futures to Hedge Commodity Exposure Futures contracts enable producers and consumers to lock in commodity prices, converting price uncert...
Tail-Risk Hedging Strategies
# Tail-Risk Hedging Strategies Tail-risk hedging protects portfolios against extreme market events—the rare but devastating drawdowns that exceed...
Stress Testing and Scenario Analysis
# Stress Testing and Scenario Analysis Stress testing evaluates portfolio performance under extreme but plausible market conditions, complementin...
Protecting Concentrated Stock Positions
# Protecting Concentrated Stock Positions Concentrated stock positions—typically from executive compensation, company founders, or inheritance—cr...
Overlay Strategies for Institutional Portfolios
# Overlay Strategies for Institutional Portfolios Overlay strategies use derivatives layered on top of existing portfolios to adjust exposures wi...
Measuring and Reporting Value at Risk
# Measuring and Reporting Value at Risk Value at Risk (VaR) quantifies the maximum expected loss over a specified time period at a given confiden...
Liquidity Considerations in Hedging Programs
# Liquidity Considerations in Hedging Programs Hedging programs require careful liquidity planning to meet margin calls, roll positions, and adju...
Interest Rate Risk Hedging with Swaps
# Interest Rate Risk Hedging with Swaps Interest rate swaps are the primary tool for managing interest rate risk in corporate treasuries and inve...
Hedge Effectiveness Testing for Accounting
# Hedge Effectiveness Testing for Accounting Hedge accounting requires demonstrating that derivatives effectively offset the risk being hedged. E...
Governance for Derivative Use Policies
# Governance for Derivative Use Policies Governance frameworks for derivatives define who can authorize trades, what instruments are permitted, h...
Glossary: Risk Management Terms
# Glossary: Risk Management Terms This glossary provides definitions for key terms used in derivatives risk management and hedging. Terms are org...
Gamma Scalping and Volatility Trading
# Gamma Scalping and Volatility Trading Gamma scalping is a trading strategy that profits from realized volatility by systematically rebalancing ...
Dynamic vs. Static Hedging Approaches
# Dynamic vs. Static Hedging Approaches Hedging strategies range from static approaches that establish positions and hold to maturity, to dynamic...
Delta Hedging Basics
# Delta Hedging Basics Delta hedging neutralizes the directional exposure of an options position by taking an offsetting position in the underlyi...
Currency Hedging for International Holdings
# Currency Hedging for International Holdings International investments carry currency risk—the value of foreign assets fluctuates with exchange ...
Counterparty Risk Management and CSA Terms
# Counterparty Risk Management and CSA Terms Counterparty risk in OTC derivatives arises when the other party may fail to meet its obligations. C...
Case Studies of Failed Hedges
# Case Studies of Failed Hedges Hedge failures have caused billions in losses and contributed to corporate bankruptcies. These failures typically...
Automation and Monitoring of Hedge Ratios
# Automation and Monitoring of Hedge Ratios Automated hedge monitoring systems track exposure-to-hedge relationships in real-time, alerting when ...
Vertical Spreads: Bull and Bear Structures
# Vertical Spreads: Bull and Bear Structures Vertical spreads combine a long option with a short option at different strikes but the same expirat...
Vega Exposure to Implied Volatility Changes
# Vega Exposure to Implied Volatility Changes Vega measures how much an option's price changes when implied volatility (IV) moves by one percenta...
Using Delta as a Hedge Ratio
# Using Delta as a Hedge Ratio Delta measures an option's sensitivity to changes in the underlying price and serves as the foundation for hedging...
Theta Decay and Time-Based Trades
# Theta Decay and Time-Based Trades Theta measures the daily loss of value in an option due to the passage of time. For option buyers, theta repr...
Straddles and Strangles for Volatility Bets
# Straddles and Strangles for Volatility Bets Straddles and strangles are volatility strategies that profit from large price movements in either ...
Rolling Strategies Pre-Expiration
# Rolling Strategies Pre-Expiration Rolling involves closing an existing options position and simultaneously opening a new one, typically at a di...
Risk Reversals and Synthetic Positions
# Risk Reversals and Synthetic Positions Risk reversals and synthetic positions use options to replicate or approximate the behavior of stock own...
Rho and Interest Rate Sensitivity
# Rho and Interest Rate Sensitivity Rho measures how much an option's price changes when interest rates change by one percentage point. While typ...
Ratio Spreads and Backspreads
# Ratio Spreads and Backspreads Ratio spreads and backspreads use unequal numbers of long and short options to create asymmetric risk/reward prof...
Protective Puts and Collars
# Protective Puts and Collars Protective puts and collars provide downside protection for long stock positions. The protective put establishes a ...
Position Greeks vs. Individual Leg Greeks
# Position Greeks vs. Individual Leg Greeks Multi-leg options strategies create complex risk profiles that differ from any single leg. Aggregatin...
Iron Condors, Butterflies, and Variations
# Iron Condors, Butterflies, and Variations Iron condors and butterflies are multi-leg strategies designed for range-bound markets. They profit w...
Horizontal and Diagonal Spread Construction
# Horizontal and Diagonal Spread Construction Horizontal (calendar) spreads and diagonal spreads use options with different expiration dates. The...
Glossary: Options Strategy Terms
# Glossary: Options Strategy Terms This glossary provides concise definitions for options strategy concepts, Greeks, and trading terms. Terms are...
Gamma and Managing Convexity
# Gamma and Managing Convexity Gamma measures how fast delta changes as the underlying moves. It represents the convexity of an option's payoff—t...
Event-Driven Volatility Trades
# Event-Driven Volatility Trades Beyond earnings, numerous scheduled events drive volatility in specific stocks or the broader market. FDA decisi...
Earnings Season Options Playbooks
# Earnings Season Options Playbooks Earnings announcements are among the most significant events for options traders. Implied volatility typicall...
Covered Calls and Cash-Secured Puts
# Covered Calls and Cash-Secured Puts Covered calls and cash-secured puts are foundational income strategies that involve selling options against...
Calendar Spreads for Income Generation
# Calendar Spreads for Income Generation Calendar spreads exploit the faster time decay of near-term options versus longer-term options. By selli...
Adjusting Options Trades Mid-Course
# Adjusting Options Trades Mid-Course Options positions rarely work out exactly as planned. When the underlying moves against you, time passes, o...
Understanding Moneyness and Delta Exposure
# Understanding Moneyness and Delta Exposure Moneyness describes where an option's strike price stands relative to the current price of the under...
Tax Considerations for Equity Options
# Tax Considerations for Equity Options Options trading creates taxable events that differ from stock transactions. Understanding when taxes appl...
Risk Disclosures Required Before Trading
# Risk Disclosures Required Before Trading Before trading options, regulations require brokers to provide risk disclosure documents and verify su...
Reg T and Portfolio Margin Treatment
# Reg T and Portfolio Margin Treatment Margin rules determine how much capital you need to trade options. Regulation T (Reg T) provides standard ...
Physical vs. Cash Settlement Differences
# Physical vs. Cash Settlement Differences Options can settle in two ways: through physical delivery of the underlying asset or through cash paym...
Options on ETFs vs. Single Stocks
# Options on ETFs vs. Single Stocks Exchange-traded fund (ETF) options and single-stock options share the same mechanics but differ in volatility...
Option Symbology on US Exchanges
# Option Symbology on US Exchanges US-listed equity options use a standardized ticker format established by the Options Clearing Corporation (OCC...
Option Contract Specifications: Strike, Expiry, Style
# Option Contract Specifications: Strike, Expiry, Style Every option contract is defined by three critical specifications: the strike price, the ...
Option Chain Layout and Key Stats
# Option Chain Layout and Key Stats The option chain displays all available options for an underlying asset, organized by expiration and strike p...
Open Interest and Volume Signals
# Open Interest and Volume Signals Volume and open interest provide insight into market activity and positioning. Volume shows today's trading ac...
Mini, Weekly, and Quarterly Options Explained
# Mini, Weekly, and Quarterly Options Explained Beyond standard monthly options, exchanges offer products with different expiration frequencies a...
LEAPS and Long-Dated Contracts
# LEAPS and Long-Dated Contracts Long-Term Equity Anticipation Securities (LEAPS) are options with expiration dates extending one to three years ...
Intrinsic Value vs. Time Value
# Intrinsic Value vs. Time Value Every option premium consists of two components: intrinsic value and time value (also called extrinsic value). U...
Glossary: Options Fundamentals
# Glossary: Options Fundamentals This glossary provides concise definitions for essential options trading terminology. Terms are organized alphab...
Corporate Action Adjustments to Options
# Corporate Action Adjustments to Options Corporate actions like stock splits, mergers, and special dividends can significantly alter the terms o...
Clearing and OCC Guarantees
# Clearing and OCC Guarantees The Options Clearing Corporation (OCC) acts as the central clearinghouse for all US-listed options. By becoming the...
Call vs. Put Options: Payoffs and Use Cases
# Call vs. Put Options: Payoffs and Use Cases Options contracts provide the right, but not the obligation, to buy or sell an underlying asset at ...
Basic Option Pricing Drivers
# Basic Option Pricing Drivers Option prices reflect six fundamental inputs: underlying price, strike price, time to expiration, volatility, inte...
Assignment, Exercise, and Expiration Logistics
# Assignment, Exercise, and Expiration Logistics When an option holder exercises their right, the Options Clearing Corporation (OCC) randomly ass...
American vs. European Exercise Rights
# American vs. European Exercise Rights Option exercise style determines when the holder can convert the option into its underlying position. Thi...
Training Programs for Derivative Users
# Training Programs for Derivative Users Training programs ensure that derivatives professionals have the knowledge and skills to perform their r...
Third-Party Vendor Management
# Third-Party Vendor Management Derivatives trading operations rely on numerous third-party vendors for trading systems, market data, clearing se...
Swap Execution Facilities and Designated Contract Markets
# Swap Execution Facilities and Designated Contract Markets The Dodd-Frank Act created swap execution facilities (SEFs) to bring transparency and...
Role of Clearinghouses and the OCC
# Role of Clearinghouses and the OCC Clearinghouses serve as central counterparties (CCPs) that stand between buyers and sellers, guaranteeing tr...
Reporting Trades Under Dodd-Frank
# Reporting Trades Under Dodd-Frank The Dodd-Frank Act requires comprehensive reporting of swap transactions to swap data repositories (SDRs). Th...
Regulation Best Interest and Derivative Sales
# Regulation Best Interest and Derivative Sales SEC Regulation Best Interest (Reg BI) establishes a standard of conduct for broker-dealers when m...
Recordkeeping and Surveillance Obligations
# Recordkeeping and Surveillance Obligations Financial firms trading derivatives must maintain comprehensive records of trading activity and cond...
Operational Risk in High-Volume Options Trading
# Operational Risk in High-Volume Options Trading High-volume options trading environments process thousands to millions of trades daily, creatin...
Onboarding New Counterparties
# Onboarding New Counterparties Counterparty onboarding establishes the legal, operational, and credit framework for derivatives trading relation...
Model Governance and Controls Requirements
# Model Governance and Controls Requirements Model governance establishes the framework for developing, validating, and monitoring quantitative m...
KYC and AML Considerations in OTC Markets
# KYC and AML Considerations in OTC Markets Know Your Customer (KYC) and Anti-Money Laundering (AML) programs are essential controls for OTC deri...
Internal Audit Checklists for Derivative Programs
# Internal Audit Checklists for Derivative Programs Internal audit provides independent assurance that derivative trading controls are operating ...
Glossary: Regulatory and Operational Terms
# Glossary: Regulatory and Operational Terms This glossary provides definitions for key regulatory and operational terms used in derivatives trad...
EMIR and MiFID Considerations for US Firms
# EMIR and MiFID Considerations for US Firms US firms trading derivatives with European counterparties must navigate both the European Market Inf...
Disaster Recovery for Trading Desks
# Disaster Recovery for Trading Desks Disaster recovery planning ensures derivatives trading operations can continue or rapidly resume following ...
Derivative Trade Lifecycle from Order to Settlement
# Derivative Trade Lifecycle from Order to Settlement The derivative trade lifecycle encompasses all stages from initial order placement through ...
Cybersecurity Considerations for Derivatives Teams
# Cybersecurity Considerations for Derivatives Teams Derivatives trading operations face significant cybersecurity risks due to high-value transa...
Compliance Testing for Position Limits
# Compliance Testing for Position Limits Position limits restrict the number of contracts a trader or entity can hold in a particular commodity o...
Collateral Optimization Strategies
# Collateral Optimization Strategies Collateral optimization involves allocating available assets to meet margin requirements at the lowest possi...
Accounting Standards ASC 815 Overview
# Accounting Standards ASC 815 Overview ASC 815 (Derivatives and Hedging) establishes accounting and reporting standards for derivative instrumen...
Using Futures for Equity Beta Exposure
# Using Futures for Equity Beta Exposure Equity index futures provide capital-efficient exposure to broad market movements. By posting margin rat...
Understanding Delivery Months and Symbols
# Understanding Delivery Months and Symbols Every futures contract has a unique symbol that identifies the underlying asset, delivery month, and ...
Tax Treatment of Section 1256 Contracts
# Tax Treatment of Section 1256 Contracts Section 1256 of the Internal Revenue Code provides special tax treatment for regulated futures contract...
Spread Margining Rules
# Spread Margining Rules Spread margining recognizes that offsetting futures positions have lower risk than outright positions. When you hold bot...
Seasonality Considerations in Futures Markets
# Seasonality Considerations in Futures Markets Many commodity futures exhibit predictable seasonal patterns driven by production cycles, weather...
Position Limits and Accountability Levels
# Position Limits and Accountability Levels Regulators and exchanges impose position limits to prevent excessive speculation and market manipulat...
Mark-to-Market Accounting Mechanics
# Mark-to-Market Accounting Mechanics Mark-to-market accounting recognizes gains and losses on futures positions daily, based on settlement price...
Margin Efficiency vs. ETFs or Swaps
# Margin Efficiency vs. ETFs or Swaps Futures, ETFs, and swaps all provide exposure to the same underlying markets, but with different capital re...
Interest Rate and Treasury Futures Primer
# Interest Rate and Treasury Futures Primer Interest rate and Treasury futures allow investors to gain or hedge exposure to interest rate movemen...
Initial and Variation Margin Process
# Initial and Variation Margin Process Margin is the financial safeguard that ensures futures contract performance. Initial margin is posted when...
Glossary: Futures Market Terms
# Glossary: Futures Market Terms This glossary provides concise definitions for futures market concepts, trading terms, and regulatory language. ...
Futures Contract Specifications and Standardization
# Futures Contract Specifications and Standardization Futures contracts are standardized agreements to buy or sell an asset at a predetermined pr...
Forward Contracts vs. Exchange-Traded Futures
# Forward Contracts vs. Exchange-Traded Futures Both forwards and futures obligate parties to buy or sell an asset at a future date, but their st...
Currency Futures for Hedging FX Risk
# Currency Futures for Hedging FX Risk Currency futures provide a standardized, exchange-traded method for hedging foreign exchange exposure. Unl...
Commodity Futures: Storage and Convenience Yield
# Commodity Futures: Storage and Convenience Yield Commodity futures pricing differs from financial futures because physical commodities incur st...
Cash vs. Physical Settlement Agreements
# Cash vs. Physical Settlement Agreements Futures contracts terminate through either cash settlement or physical delivery. Cash settlement involv...
Calendar Spreads and Roll Strategies
# Calendar Spreads and Roll Strategies Futures contracts expire, requiring traders with ongoing exposure to periodically roll positions from expi...
Block Trades and Exchange for Physical
# Block Trades and Exchange for Physical Large institutional orders can move markets significantly. Block trades and exchange for physical (EFP) ...
Basis Risk Between Futures and Spot
# Basis Risk Between Futures and Spot Basis risk is the risk that futures prices won't move in perfect lockstep with the asset being hedged. Unde...
Backtesting Futures Trading Systems
# Backtesting Futures Trading Systems Backtesting uses historical data to evaluate how a trading strategy would have performed. For futures, back...
Volatility Term Structure Modeling
# Volatility Term Structure Modeling Volatility term structure modeling connects near-term events to long-term vol regimes—similar to yield-curve...
Stress Testing Models for Extreme Moves
# Stress Testing Models for Extreme Moves The March 2020 COVID crash and the 2018 volatility spike (Volmageddon) demonstrated that models calibra...
Smile and Skew Interpretation
# Smile and Skew Interpretation Volatility smiles and skews function like a seismograph for market sentiment—recording fear, complacency, and pos...
Put-Call Parity Applications
# Put-Call Parity Applications Put-call parity is a currency converter between payoffs—transforming calls into puts and stock into synthetics thr...
Pricing Dividend-Paying Underlyings
# Pricing Dividend-Paying Underlyings Dividends reduce stock prices on ex-dates, directly affecting option values. Models must incorporate these ...
Open-Source Tools for Derivative Pricing
# Open-Source Tools for Derivative Pricing Open-source libraries provide a valuable toolbox for derivative pricing—tested implementations of comp...
No-Arbitrage Principles in Derivatives
# No-Arbitrage Principles in Derivatives Arbitrage-free pricing rests on the premise that identical payoffs must have identical prices, within a ...
Monte Carlo Simulation Techniques
# Monte Carlo Simulation Techniques Monte Carlo simulation prices derivatives by simulating many possible paths of the underlying and averaging t...
Model Risk Governance Practices
# Model Risk Governance Practices Model risk governance ensures that derivative pricing models are developed, validated, and monitored according ...
Model Calibration and Validation
# Model Calibration and Validation Model calibration fits parameters to market data; validation confirms the model performs adequately for its in...
Local vs. Stochastic Volatility Models
# Local vs. Stochastic Volatility Models Choosing between local and stochastic volatility models is like selecting between GPS navigation and wea...
Interest Rate Model Families
# Interest Rate Model Families Selecting an interest rate model is like choosing an engine for different aircraft—short-rate models power simple ...
Implied Volatility Surface Basics
# Implied Volatility Surface Basics The implied volatility surface maps how implied volatility varies across strikes and expirations—a topography...
Glossary: Derivative Pricing Terminology
# Glossary: Derivative Pricing Terminology This glossary provides concise definitions of derivative pricing terms used throughout the Derivative ...
Finite Difference Methods Overview
# Finite Difference Methods Overview Finite difference methods solve the Black-Scholes PDE on a discrete grid—a mesh net of spot prices and time ...
Estimating Greeks Numerically
# Estimating Greeks Numerically When closed-form Greeks aren't available—complex payoffs, stochastic volatility models, or path-dependent options...
Black-Scholes Model Inputs and Outputs
# Black-Scholes Model Inputs and Outputs The Black-Scholes model transforms five inputs into an option price and a set of risk sensitivities (Gre...
Binomial Trees for Option Pricing
# Binomial Trees for Option Pricing Binomial trees decompose option pricing into a sequence of discrete decisions—like climbing a decision ladder...
Backtesting Pricing Models Against Market Data
# Backtesting Pricing Models Against Market Data Backtesting replays historical market conditions through a pricing model to measure accuracy aga...
American Option Pricing Approaches
# American Option Pricing Approaches Pricing American options requires solving a free-boundary problem—at each point in time, the holder decides ...