Implied Volatility Measures Research Articles

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Robust Artificial Neural Networks for Pricing of European Options

The option pricing ability of Robust Artificial Neural Networks optimized with the Huber function is compared against those optimized with Least Squares. Comparison is in respect to pricing European call options on the S&P 500 using daily data for the period April 1998 to August 2001. The analysis is augmented with the use of several historical and implied volatility measures. Implied volatilities are the overall average, and the average per maturity. Beyond the standard neural networks, hybrid networks that directly incorporate information from the parametric model are included in the analysis. It is shown that the artificial neural network models with the use of the Huber function outperform the ones optimized with least squares.

A framework for decomposing shocks and measuring volatilities derived from multi-dimensional panel data of survey forecasts

This work applies previously published frameworks developed for analyzing multi-dimensional panel data of survey forecasts to IPD forecasts from the Survey of Professional Forecasters. The paper expands on these frameworks, demonstrates that the frameworks imply the existence of new and richer measures of shocks and volatilities, and shows how these measures can be extracted from multi-dimensional forecast panels. Three distinct types of economic shocks (cumulative shocks, cross-sectional shocks, and discrete shocks) and implied volatility measures based on these shocks are calculated for IPD inflation over the period 1969 through 2004. GMM tests for forecaster biases are conducted using the expanded framework.

Estimating Dynamics of S&P 500 Index and Volatility Using Option Market Data

This paper studies the joint dynamics of the daily return on the S&P 500 index and its volatility using the option market data. We construct a measure of the stock return volatility based on the Black-Scholes implied volatilities of exchange traded options. The implied volatility measure is shown to be an efficient proxy of the daily stock return volatility as it dominates the conditional volatility estimate obtained from the GARCH models. Using the time series of the implied volatility, we examine the goodness-of-fit of several existing stochastic volatility models and find that a CEV specification with non-linear drift fits the data well. We further estimate a jump-diffusion model of stock return and volatility. We present evidence that both stock return and volatility processes contain jumps and the jump sizes in return and volatility are negatively correlated. We also investigate the information content of two implied volatility related variables: the slope of volatility smile and the term structure of implied volatility. We find evidence that the slope can predict future stock returns while both slope and term structure can predict future volatilities.

Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements

Abstract The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper, we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First, we consider unobserved components (UC-RV) and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility (SV) models and generalised autoregressive conditional heteroskedasticity (GARCH) models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 (S&P 100) stock index series for which trading data (tick by tick) of almost 7 years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.

Forecasting Daily Variability of the S&P 100 Stock Index Using Historical, Realised and Implied Volatility Measurements

The increasing availability of financial market data at intraday frequencies has not only led to the development of improved volatility measurements but has also inspired research into their potential value as an information source for volatility forecasting. In this paper we explore the forecasting value of historical volatility (extracted from daily return series), of implied volatility (extracted from option pricing data) and of realised volatility (computed as the sum of squared high frequency returns within a day). First we consider unobserved components and long memory models for realised volatility which is regarded as an accurate estimator of volatility. The predictive abilities of realised volatility models are compared with those of stochastic volatility models and generalised autoregressive conditional heteroskedasticity models for daily return series. These historical volatility models are extended to include realised and implied volatility measures as explanatory variables for volatility. The main focus is on forecasting the daily variability of the Standard & Poor's 100 stock index series for which trading data (tick by tick) of almost seven years is analysed. The forecast assessment is based on the hypothesis of whether a forecast model is outperformed by alternative models. In particular, we will use superior predictive ability tests to investigate the relative forecast performances of some models. Since volatilities are not observed, realised volatility is taken as a proxy for actual volatility and is used for computing the forecast error. A stationary bootstrap procedure is required for computing the test statistic and its p-value. The empirical results show convincingly that realised volatility models produce far more accurate volatility forecasts compared to models based on daily returns. Long memory models seem to provide the most accurate forecasts.

An Empirical-Distribution-Based Option Pricing Model: A Solution to the Volatility Smile Puzzle

The volatility smile that is generated by the Black-Scholes model has been traditionally attributed to an inappropriately assumed return distribution. Previous studies use alternative specifications such as stochastic volatility and jump diffusion models. However, these specifications do not eliminate the smile. Moreover, as documented by Das and Sundaram (1999), the return distributions that are generated by stochastic volatility and jump diffusion models do not match important characteristics of realized returns. We construct an alternative valuation procedure to price S&P 500 call options, using a histogram from past S&P 500 index daily returns. We find that the implied volatilities that are generated by our model do not exhibit substantial relationship to moneyness levels. Consistent with the absence of the smile, payoffs to holding options are also not related to moneyness levels. We also find that these payoffs are more closely related to our implied volatility measures than to the Black Scholes implied volatility measures. These findings indicate that our model is more appropriate than the Black-Scholes model to value S&P 500 call options.

The Relationship Between Implied and Realized Volatility in the Danish Option and Equity Markets

In this paper we examine the information content of options on the Danish KFX share index. These options are traded very infrequently and with a low volume. We consider the relationship between the volatility implied in an option's price and the subsequently realized volatility. Recently, Christensen and Prabhala (1998) find that implied volatility in at-the-money one month OEX call options on the S&P100 index is an unbiased and efficient forecast of ex-post realized index volatility after the 1987 stock market crash. Gwilym and Buckle (1999) study the UK FTSE100 index and find that although historical volatility estimates have greater accuracy, implied volatility contains more information, based on regression tests, in particular when very short maturities are avoided. In this paper we investigate whether the UK and US markets are special, and whether the infrequent trading and low volume in the KFX case lead to bias and inefficiency in the implied volatility forecast. We examine one month at-the-money KFX calls and similar puts, and we introduce an implied volatility measure that combines information from both call and put prices. We find that implied volatility indeed contains information about realized index return volatility. In fact, implied volatility remains significant even in the multiple regression where historical volatility is included, it subsumes the information content of this, and the bias in the implied volatility forecast is insignificant. The results suggest that the finding in the OEX market may be extended to the much smaller KFX market.