Implied Volatility Surface: Construction Methodologies and Characteristics

TL;DR

This paper surveys various methodologies for constructing implied volatility surfaces, discussing practical considerations like arbitrage constraints, extrapolation, calibration, and surface dynamics to improve their accuracy and reliability.

Contribution

It provides a comprehensive overview of construction techniques and practical issues affecting the implementation of implied volatility surfaces in finance.

Findings

Various construction methodologies are compared and analyzed.

Practical issues like arbitrage constraints and extrapolation are discussed.

Guidelines for calibration and modeling of volatility surface dynamics are provided.

Abstract

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.