101 Concepts for the Level I Exam

Concept 90: Use of Arbitrage, Replication, and Risk Neutrality in Pricing Derivatives

Arbitrage is the condition under which two equivalent assets or derivatives or combination of assets and derivatives sell for different prices.

  • This allows an arbitrageur to buy at a low price and sell at a high price, and earn a risk-free profit from this transaction without committing any capital.
  • In well-functioning markets, arbitrage opportunities are quickly exploited. The combined actions of arbitrageurs force the prices of similar securities to converge. Hence, arbitrage leads to the law of one price: securities or derivatives that produce equivalent results must sell for equivalent prices.

Replication is the creation of an asset or a portfolio from another asset, portfolio, and/or derivative. Example: stock + short forward = risk-free asset.

Risk neutrality:  The risk aversion of an individual does not impact derivative pricing. The risk-free rate is used for pricing derivatives.

The overall process of pricing derivatives by arbitrage and risk neutrality is called arbitrage-free pricing. According to this process,

  • A derivative must be priced such that no arbitrage opportunities exist, and there can only be one price for the derivative that earns the risk-free return.
  • Asset + Derivative = Risk-free asset