Derivatives

Derivatives are financial instruments whose value derives from an underlying asset, rate, or index. This section introduces fundamental derivative characteristics including the underlying asset, contract specifications, and settlement procedures. Derivative markets are divided into exchange-traded (standardized, centrally cleared) and over-the-counter (customized, bilateral) segments. Each market structure has distinct advantages regarding customization, liquidity, transparency, and counterparty risk.

Key Concepts Covered:

• Definition and basic features of derivative instruments
• Derivative underlying assets: stocks, bonds, currencies, commodities, indexes
• Exchange-traded derivatives: standardization, clearinghouse, transparency
• Over-the-counter (OTC) derivatives: customization and bilateral risk
• Comparative advantages of exchange vs. OTC markets

Derivatives fall into two major categories: forward commitments and contingent claims. Forward commitments (forwards, futures, swaps) obligate both parties to transact in the future. Contingent claims (options, credit derivatives) give the holder a right but not an obligation. This section defines each instrument type and compares their characteristics. Understanding option payoffs at expiration - both value and profit - is fundamental to option analysis.

Key Concepts Covered:

• Forward commitments: forwards, futures, swaps (obligations for both parties)
• Contingent claims: call and put options, credit derivatives (rights not obligations)
• Comparing characteristics across derivative types
• Option payoffs at expiration: intrinsic value calculations
• Option profits accounting for premium paid

Derivatives serve important economic functions while creating unique risks. Benefits include risk management (hedging), price discovery, operational efficiency, and market completeness. Risks include leverage magnifying losses, complexity obscuring true exposures, and counterparty credit risk. Different market participants - corporations, financial institutions, asset managers, speculators - use derivatives for hedging, income generation, arbitrage, or speculation with varying objectives.

Key Concepts Covered:

• Benefits: risk management, price discovery, operational efficiency, leverage
• Risks: magnified losses, complexity, counterparty default, liquidity
• Corporate issuer uses: hedging commodity prices, interest rates, FX
• Investor uses: portfolio hedging, income enhancement, tactical positioning
• Speculation vs. hedging: objectives and risk profiles

Arbitrage and replication are fundamental pricing concepts in derivatives. No-arbitrage pricing ensures derivative prices prevent riskless profitable trades. Replication creates synthetic positions matching derivative payoffs using underlying assets and risk-free borrowing. Cost of carry represents the net cost of holding the underlying asset (storage, financing costs minus benefits like dividends). These concepts establish pricing relationships between derivatives and their underlyings.

Key Concepts Covered:

• No-arbitrage principle in derivative pricing
• Replication: creating synthetic positions matching derivative payoffs
• Cost of carry: storage and financing costs minus income/convenience yield
• Relationship between spot prices, forward prices, and carrying costs
• Arbitrage bounds on derivative prices

Forward contract pricing and valuation differ across the contract's life. At initiation, forwards are typically priced at zero value with no upfront payment. During the contract life, value fluctuates with changes in the underlying price. At expiration, value equals the difference between spot and forward prices. Interest rate forward contracts (FRAs) have specialized pricing using forward rates from the yield curve, with applications in hedging future borrowing or lending.

Key Concepts Covered:

• Forward pricing at initiation: zero-value pricing formula
• Forward valuation during contract life as underlying prices change
• Expiration value and settlement mechanisms
• Forward rate agreements (FRAs) for interest rate risk
• Uses of forward rates in hedging and speculation

Futures contracts are economically similar to forwards but have important differences. Daily settlement (marking-to-market) creates different cash flow patterns than forwards. Margin requirements and daily settlement affect futures pricing relative to forwards. Convergence of futures prices to spot prices at expiration ensures contract integrity. Understanding these mechanics explains why futures and forward prices can differ even for identical underlyings and maturities.

Key Concepts Covered:

• Futures vs. forwards: daily settlement and margin requirements
• Marking-to-market cash flows and their pricing implications
• Why futures and forward prices differ: interest rate effects
• Convergence of futures price to spot price at expiration
• Basis: spot price minus futures price dynamics

Swaps are agreements to exchange cash flows over time, similar to a series of forward contracts but with unified terms. This section examines how swaps combine multiple forward obligations into a single contract. The distinction between swap value (market value) and swap price (the fixed rate or spread) is important. Interest rate swaps are the most common type, but currency swaps and other variants serve different hedging and investment purposes.

Key Concepts Covered:

• Swap structure: series of forward contracts with unified terms
• Interest rate swaps: fixed vs. floating cash flow exchanges
• Swap pricing: determining the fixed rate at initiation
• Swap valuation: changes in market value over contract life
• Currency swaps and other swap variations

Option values comprise intrinsic value (exercise value) and time value (value beyond intrinsic value). Moneyness describes an option's relationship to the underlying price (in-the-money, at-the-money, out-of-the-money). Unlike forward commitments, options require more sophisticated pricing due to their asymmetric payoffs. Six primary factors affect option values: underlying price, exercise price, time to expiration, volatility, risk-free rate, and income on the underlying. Understanding how each factor impacts value is crucial.

Key Concepts Covered:

• Intrinsic value vs. time value components of option prices
• Moneyness: in-the-money, at-the-money, out-of-the-money
• Six factors affecting option values and their directional impacts
• Underlying price and exercise price effects on calls vs. puts
• Time decay, volatility, interest rates, and income effects

Put-call parity is a no-arbitrage relationship linking European call and put option prices for the same underlying, strike, and expiration. This powerful relationship allows synthetic replication of any option position using combinations of the other three components (call, put, underlying, risk-free bond). Put-call forward parity extends this relationship to options on forwards. These parity relationships enable arbitrage trading, option pricing validation, and flexible position construction.

Key Concepts Covered:

• Put-call parity relationship for European options
• Synthetic positions: creating calls from puts or vice versa
• Arbitrage opportunities when parity is violated
• Put-call forward parity for options on forward contracts
• Applications in trading, hedging, and pricing validation

The binomial model provides an intuitive framework for option pricing. In a one-period model, the underlying can move to only two possible prices (up or down). Creating a replicating portfolio of the underlying and risk-free borrowing matches the option payoff in both states, determining the option's fair value. Risk-neutral pricing simplifies calculations by treating expected returns as the risk-free rate. This foundational model extends to multiple periods for more realistic scenarios.

Key Concepts Covered:

• One-period binomial model framework: two possible outcomes
• Replicating portfolio approach to option valuation
• Calculating hedge ratios and option values
• Risk-neutral pricing: using risk-free rate for expectation
• Extension to multi-period models and American options