Empirical performance of a spline-based implied volatility surface

Implied volatility surface

The widespread practice of quoting option prices in terms of their Black-Scholes implied volatilities (IVs) in no way implies that market participants believe underlying returns to be lognormal. On the contrary, the variation of IVs across option strike and term to maturity, which is widely referred to as the volatility surface, can be substantial. In this brief review, we highlight some empiri...

Implied Volatility Surface Construction

Implied volatility surfaces are central tools used for pricing options. This thesis treats the topic of their construction. The main purpose is to uncover the most appropriate methodology for constructing implied volatility surfaces from discrete data and evaluate how well it performs. First some methods and techniques in use for such surface constructing are presented. Then the most attractive...

Implied volatility functions: empirical tests

Black and Scholes (1973) implied volatilities tend to be systematically related to the option’s exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset’s return is a de...

Implied and Realized Volatility: Empirical Model Selection

The paper studies the nonparametric connection between realized and implied volatilities. No-arbitrage identities and comparison inequalities are found. We formulate the multi-factor trading system on the volatility scale. To empirically determine the number of factors, we develop a high frequency analysis for sequential F-testing. We also design a cross validated estimate of quadratic variation.

Deformation of Implied Volatility Surfaces: An Empirical Analysis