The aim of this paper is to price an American style option when there is uncertainty on the volatility of the underlying asset. An option contract can be either European or American style depending on whether the exercise is possible only at or also before the expiry date. A European option gives the holder the right to buy or sell the underlying asset only at the expiry date of the option. On ...

Dumas, Fleming, Whaley (DFW, 1998) find that option models based on deterministic volatility functions (DVF) perform poorly because the estimated volatility function is unstable over time. DFW provide evidence that the DVF changes significantly on a weekly basis. This paper proposes a new class of dynamic implied volatility function models (DIVF). This class of models separates a time-invariant...

This paper assesses the robustness of the relative performance of spotand optionsbased volatility forecasts to the treatment of microstructure noise. Robustness of the results to the method of constructing option-implied forecasts is also investigated. Using a test for superior predictive ability, model-free implied volatility, which exploits information in the volatility ‘smile’, and at-the-mo...

This paper provides a simple unified framework for assessing the empirical linkages between returns and realized and implied volatilities. First, we show that whereas the volatility feedback effect as measured by the sign of the correlation between contemporaneous return and realized volatility depends importantly on the underlying structural model parameters, the correlation between return and...

We present an Hilbert space formulation for a set of implied volatility models introduced in [3] in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price T an K, to be arbitrage free. The arbitrage free conditions give a system of stochastic PDEs for the evolution of the implied volatility surface σ̂t(T,K). We will focus on the...

We propose a market-based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of an implied volatility surface by representing it as a randomly fluctuating surface driven by a finite number of orthogonal random...

Consistent with findings in other markets, implied volatility is a biased predictor of the realized volatility of gold futures. No existing explanation—including a price of volatility risk— can completely explain the bias, but much of this apparent bias can be explained by persistence and estimation error in implied volatility. Statistical criteria reject the hypothesis that implied volatility ...

German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after calibrating for the Merton jump diffusion (MJD), variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman, Madan and Yor (CGMY) and the Black and Scholes (B&S) model. Implied volatility is examined...

We construct a risk-neutral stochastic volatility model using no-arbitrage pricing principles. We then study the behavior of the implied volatility of options that are deep in and out of the money according to this model. The motivation of this study is to show the diierence in the asymptotic behavior of the distribution tails between the usual Black-Scholes log-normal distribution and the risk...