Implied Volatility Surface: Construction Methodologies and Characteristics

Understand

The implied volatility surface (IVS) is a fundamental building block in computational finance.

• We provide a survey of methodologies for constructing such surfaces.
• We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both strike and time, how to perform extrapolation outside the core region, choice of calibrating functional and selection of numerical optimization algorithms, volatility surface dynamics and asymptotics.