Perfect replication and when markets lack it
Question
What is the difference between a complete market and an incomplete market?
Short answer
In a complete market every contingent claim can be replicated by trading available assets, so each has a unique no-arbitrage price; in an incomplete one some cannot. Black-Scholes is complete. Stochastic volatility, jumps or untraded risks (e.g. weather) make markets incomplete: there are many risk-neutral measures, so no-arbitrage gives a price range and extra assumptions, such as a market price of risk or a utility function, are needed.
Adapted from Wilmott, Frequently Asked Questions in Quantitative Finance, FAQ 32, p.146; question and answer rewritten by SelfMadeQuant.com.
See the hint and the full worked solution in the question bank (free account).
Open the worked solutionLessons behind this question
- The Law of One Price and Replication: No-Arbitrage Pricing from First Principles
- The One-Period Binomial Model: Replication, Delta Hedging, and Risk-Neutral Pricing
Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.
Read it free