In complete markets, every possible outcome has a corresponding financial instrument, facilitating total risk mitigation. This environment is free of arbitrage and optimally processes market information. Nonetheless, achieving perfect market completeness is often elusive in practice.
Definition
A complete market refers to a setting where there exists a financial instrument (e.g., a security or contract) for every possible outcome. This means every potential risk can be hedged.
State Prices
- In a complete market, there is a unique set of state prices for every potential future state of the world.
- State prices represent the present value of a payoff that would occur in a specific future state.
Arbitrage-Free Market
A foundational concept to complete markets is the absence of arbitrage opportunities. If arbitrage were present, prices would adjust until it no longer exists.
Complete vs. Incomplete Markets
In an incomplete market, not all risks can be hedged due to the absence of some financial instruments. This contrasts with the complete market where every conceivable risk has an associated instrument.
Market Efficiency
- Efficient Market Hypothesis (EMH) posits that asset prices fully reflect all available information.
- A complete market is more likely to be efficient, as there are more instruments to convey and process information.
Role of Financial Intermediaries
- These entities exist to create and offer the variety of financial instruments that complete the market.
- Examples include banks, investment firms, and insurance companies.
Hedging and Risk Sharing
- In a complete market, entities can hedge any risk by buying the appropriate financial instrument.
- Risk sharing becomes seamless, as participants can offload or take on risks as desired.
Implications for Portfolio Theory
- In a complete market, an investor can achieve any desired risk-return trade-off using available securities.
- The existence of a unique risk-free rate is also ensured.
Mathematical Framework
The Martingale Measure or Risk-Neutral Measure is a mathematical tool used to price derivatives in complete markets. It adjusts the probabilities of future states to a “risk-neutral world” where all assets are expected to grow at the risk-free rate.
Global Perspective
- While individual markets (e.g., the stock market in a particular country) might be closer to completion than others, globally, many markets still exhibit signs of incompleteness due to various frictions.
- Globalization and technological advancement are driving factors behind the creation of new financial instruments, pushing markets closer to completion.
Regulation and Market Completion
- Regulatory frameworks can either aid or hinder market completeness.
- While certain regulations can foster the creation of new financial instruments, others can inhibit them due to concerns about complexity, transparency, or systemic risks.
Limitations and Criticisms
- Real-world markets are seldom perfectly complete. Market frictions, information asymmetry, and transaction costs can prevent full completion.
- Some scholars argue that excessive financial innovation, aiming for market completion, can introduce systemic risks.
Economic Implications
- A complete market theoretically supports optimal resource allocation, as risks are priced accurately.
- Financial crises can be interpreted, in part, as manifestations of market incompleteness.
