The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with constant volatility models up to stochastic volatility. We also survey less commonly known models e.g. hybrid models. We explain various volatility types (e....

This paper examines a variety of methods for extracting implied probability distributions from option prices and the underlying. The paper first explores nonparametric procedures for reconstructing densities directly from options market data. I then consider local volatility functions, both through implied volatility trees and volatility interpolation. I then turn to alternative specifications ...

This paper examines a variety of methods for extracting implied probability distributions from option prices and the underlying. The paper …rst explores non-parametric procedures for reconstructing densities directly from options market data. I then consider local volatility functions, both through implied volatility trees and volatility interpolation. I then turn to alternative speci…cations o...

The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space allowing for a low dimensional factor representation of th...

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.

In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied Black-Scholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities. The conditions are derived that have to be satisfied to ensure absence of arbitrage in the model and ...