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Volatility smile
About: Volatility smile is a research topic. Over the lifetime, 8702 publications have been published within this topic receiving 318440 citations.
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TL;DR: In this paper, the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns is modified to allow for volatility feedback effect, which amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes.
Abstract: It is sometimes argued that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. This paper modifies the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns to allow for this volatility feedback effect. The resulting model is asymmetric, because volatility feedback amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes. The model also implies that volatility feedback is more important when volatility is high. In U.S. monthly and daily data in the period 1926-88, the asymmetric model fits the data better than the standard GARCH model, accounting for almost half the skewness and excess kurtosis of standard monthly GARCH residuals. Estimated volatility discounts on the stock market range from 1% in normal times to 13% after the stock market crash of October 1987 and 25% in the early 1930's. However volatility feedback has little effect on the unconditional variance of stock returns.
1,793 citations
Posted Content•
TL;DR: In this paper, the short run interdependence of prices and price volatility across three major international stock markets is studied using the autoregressive conditionally heteroskedastic (ARCH) family of statistical models.
Abstract: The short-run interdependence of prices and price volatility across three major international stock markets is studied. Daily opening and closing prices of major stock indexes for the Tokyo, London, and New York stock markets are examined. The analysis utilizes the autoregressive conditionally heteroskedastic (ARCH family of statistical models to explore these pricing relationships. Evidence of price volatility spillovers from New York to Tokyo, London to Tokyo, and New, York to London is observed but no price volatility spillover effects in other directions are found for the pre-October 1987 period.
1,780 citations
TL;DR: In this paper, an efficient method was developed for pricing American options on stochastic volatility/jump-diffusion processes under systematic jump and volatility risk, and the parameters implicit in deutsche mark (DM) options of the model and various submodels were estimated over the period 1984 to 1991 via nonlinear generalized least squares, and tested for consistency with $/DM futures prices and the implicit volatility sample path.
Abstract: An efficient method is developed for pricing American options on stochastic volatility/jumpdiffusion processes under systematic jump and volatility risk. The parameters implicit in deutsche mark (DM) options of the model and various submodels are estimated over the period 1984 to 1991 via nonlinear generalized least squares, and are tested for consistency with $/DM futures prices and the implicit volatility sample path. The stochastic volatility submodel cannot explain the "volatility smile" evidence of implicit excess kurtosis, except under parameters implausible given the time series properties of implicit volatilities. Jump fears can explain the smile, and are consistent with one 8 percent DM appreciation "outlier" observed over the period 1984 to 1991. The central empirical issues in option pricing are what distributional hypotheses are consistent with observed option prices, and whether those distributional hypotheses are consistent with the properties of the un
1,777 citations
TL;DR: In this paper, the authors consider three explanations for the volatility of asset prices during exchange trading hours than during non-trading hours: public information which is more likely to arrive during normal business hours, private information which affects prices when informed investors trade, and pricing errors that occur during trading.
1,740 citations
TL;DR: In this article, the authors examined the joint time series of the S&P 500 index and near-the-money short-dated option prices with an arbitrage-free model, capturing both stochastic volatility and jumps.
1,638 citations