In financial mathematics, the implied volatility of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes) will return a theoretical value equal to the current market price of the option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security.

This document explores this concept and includes the following topics:

• The need for numerical calculations
• Interpretation and applications
• From option data to volatility surfaces with Maple
• Local volatility

This is part 19 of a 45-document course on Modeling Financial Markets.