This note explores the behaviour of the implied volatility of a European call option far frommaturity. Asymptotic formulae are derived with precise control over the error terms. The connection between the asymptotic implied volatility and the cumulant generating function of the logarithm of the underlying stock price is discussed in detail and illustrated by examples.

We derive closed-form analytical approximations in terms of series expansions for option prices and implied volatilities in a 2-hypergeometric stochastic volatility model with correlated Brownian motions. As in [4], these expansions allow us to recover the well-known skew and smile phenomena on implied volatility surfaces, depending on the values of the correlation parameter.

The efficient market hypothesis based primarily on the statistical principle of Bayesian inference has been proved to be only a special-case scenario. The generalized financial market, modeled as a binary, stochastic system capable of attaining one of two possible states (High  1, Low  0) with finite probabilities, is shown to reach efficient equilibrium with p . M = p if and only if the tran...

Much research has investigated the differences between option implied volatilities and econometric model-based forecasts in terms of forecast accuracy and relative informational content. Implied volatility is a market determined forecast, in contrast to model-based forecasts that employ some degree of smoothing to generate forecasts. Therefore, implied volatility has the potential to reflect in...

This note explores the analogy between the dynamics of the interest rate term structure and the implied volatility surface of a stock. In particular, we prove an impossibility theorem conjectured by Steve Ross. Implied volatility and smile asymptotics and long rates JEL Classification: G13 Mathematics Subject Classification (2000): 60G44, 91B70

Credit default swaps (CDS) are similar to out-of-the-money put options in that both offer a low cost and effective protection against downside risk. This study investigates whether put optionimplied volatility is an important determinant of CDS spreads. Using a large sample of firms with both CDS and options data, we find that individual firms’ put option-implied volatility dominates historical...

We investigate empirically the role of trading volume (1) in predicting the relative informativeness of volatility forecasts produced by autoregressive conditional heteroskedasticity (ARCH) models versus the volatility forecasts derived from option prices, and (2) in improving volatility forecasts produced by ARCH and option models and combinations of models. Daily and monthly data are explored...

This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between options on LETFs with different leverage ratios. We first examine from empirical data the implied volatility surfaces for LETFs based on the S&P 500 index, and we introduce the concept of moneyness scaling to enhance the...

We forecast realized volatility extending the heterogeneous autoregressive model (HAR) to include implied (IV), leverage effect, overnight returns, and of volatility. analyze 10 international stock indices finding that, although a simple HAR augmented with IV (HAR-IV) is more accurate than any excluding it, all markets support further extensions HAR-IV model. More forecasts are found using retu...

The information content of option prices on the underlying asset has a special importance in finance. In particular, with the use of option implied trees, market participants may price other derivatives, estimate and forecast volatility (see e.g. the volatility index VIX), or higher moments of the underlying asset distribution. A crucial input of option implied trees is the estimation of the sm...