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228
DeltaHedged Gains and the Negative Market Volatility Risk Premium
 The Review of Financial Studies
, 2001
"... We investigate whether the volatility risk premium is negative by examining the statistical properties of deltahedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility r ..."
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Cited by 73 (3 self)
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We investigate whether the volatility risk premium is negative by examining the statistical properties of deltahedged option portfolios (buy the option and hedge with stock). Within a stochastic volatility framework, we demonstrate a correspondence between the sign and magnitude of the volatility risk premium and the mean deltahedged portfolio returns. Using a sample of S&P 500 index options, we provide empirical tests that have the following general results. First, the deltahedged strategy underperforms zero. Second, the documented underperformance is less for options away from the money. Third, the underperformance is greater at times of higher volatility.Fourth, the volatility risk premium significantly affects deltahedged gains even after accounting for jumpfears. Our evidence is supportive of a negative market volatility risk premium.
The Finite Moment Log Stable Process and Option Pricing
, 2002
"... We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sh ..."
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Cited by 69 (12 self)
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We document a surprising pattern in market prices of S&P 500 index options. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.
Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options
, 2001
"... This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the riskneutra ..."
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Cited by 66 (9 self)
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This article provides several new insights into the economic sources of skewness. First, we document the differential pricing of individual equity options versus the market index, and relate it to variations in return skewness. Second, we show how risk aversion introduces skewness in the riskneutral density. Third, we derive laws that decompose individual return skewness into a systematic component and an idiosyncratic component. Empirical analysis of OEX options and 30 stocks demonstrates that individual riskneutral distributions differ from that of the market index by being far less negatively skewed. This paper explains the presence and evolution of riskneutral skewness over time and in the crosssection of individual stocks.
The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures
 MATHEMATICAL FINANCE – BACHELIER CONGRESS 2000, GEMAN
, 1998
"... Statistical analysis of data from the nancial markets shows that generalized hyperbolic (GH) distributions allow a more realistic description of asset returns than the classical normal distribution. GH distributions contain as subclasses hyperbolic as well as normal inverse Gaussian (NIG) distributi ..."
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Cited by 63 (13 self)
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Statistical analysis of data from the nancial markets shows that generalized hyperbolic (GH) distributions allow a more realistic description of asset returns than the classical normal distribution. GH distributions contain as subclasses hyperbolic as well as normal inverse Gaussian (NIG) distributions which have recently been proposed as basic ingredients to model price processes. GH distributions generate in a canonical way Levy processes, i.e. processes with stationary and independent increments. We introduce a model for price processes which is driven by generalized hyperbolic Levy motions. This GH model is a generalization of the hyperbolic model developed by Eberlein and Keller (1995). It is incomplete. We derive an option pricing formula for GH driven models using the Esscher transform as martingale measure and compare the prices with classical BlackScholes prices. The objective of this study is to examine the consistency of our model assumptions with the empirically obser...
Maximum likelihood estimation for stochastic volatility models
 JOURNAL OF FINANCIAL ECONOMICS
, 2007
"... We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure ..."
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Cited by 62 (3 self)
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We develop and implement a method for maximum likelihood estimation in closedform of stochastic volatility models. Using Monte Carlo simulations, we compare a full likelihood procedure, where an option price is inverted into the unobservable volatility state, to an approximate likelihood procedure where the volatility state is replaced by proxies based on the implied volatility of a shortdated atthemoney option. The approximation results in a small loss of accuracy relative to the standard errors due to sampling noise. We apply this method to market prices of index options for several stochastic volatility models, and compare the characteristics of the estimated models. The evidence for a general CEV model, which nests both the affine Heston model and a GARCH model, suggests that the elasticity of variance of volatility lies between that assumed by the two nested models.
Option Pricing by Transform Methods: Extensions, Unification, and Error Control
 Journal of Computational Finance
"... We extend and unify Fourieranalytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorith ..."
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Cited by 59 (6 self)
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We extend and unify Fourieranalytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorithms to select efficient quadrature parameters and to price with guaranteed numerical accuracy.
Optionimplied Riskneutral Distributions and Implied Binomial Trees: A Literature Review
 JOURNAL OF DERIVATIVES
, 1999
"... In this partial and selective literature review of option implied riskneutral distributions and of implied binomial trees, we start by observing that in efficient markets, there is information contained in option prices, which might help us to design option pricing models. To this end, we review ..."
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Cited by 54 (3 self)
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In this partial and selective literature review of option implied riskneutral distributions and of implied binomial trees, we start by observing that in efficient markets, there is information contained in option prices, which might help us to design option pricing models. To this end, we review the numerous methods of recovering riskneutral probability distributions from option prices at one particular timetoexpiration and their applications. Next, we extend our attention beyond one timetoexpiration to the construction of implied binomial trees, which model the stochastic process of the underlying asset. Finally, we describe extensions of implied binomial trees, which incorporate stochastic volatility, as well as other nonparametric methods.
What Type of Process Underlies Options? A Simple Robust Test
, 2002
"... We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of atthemoney and outofthemoney options as the option maturity approaches zero. We show that these prices converge to ze ..."
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Cited by 50 (5 self)
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We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of atthemoney and outofthemoney options as the option maturity approaches zero. We show that these prices converge to zero at speeds which depend upon whether the sample path of the underlying asset price process is purely continuous, purely discontinuous, or a mixture of both. By applying the test to S&P 500 index options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump component. In particular, we find that while the presence of the jump component varies strongly over time, the presence of the continuous component is constantly felt. We investigate the implications of the evidence for parametric model specifications.
Forecasting crashes: Trading volume, past returns and conditional skewness in stock prices
 JOURNAL OF FINANCIAL ECONOMICS
, 2001
"... This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of crosssectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: ..."
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Cited by 50 (3 self)
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This paper is an investigation into the determinants of asymmetries in stock returns. We develop a series of crosssectional regression specifications which attempt to forecast skewness in the daily returns of individual stocks. Negative skewness is most pronounced in stocks that have experienced: 1) an increase in trading volume relative to trend over the prior six months; and 2) positive returns over the prior thirtysix months. The first finding is consistent with the model of Hong and Stein (1999), which predicts that negative asymmetries are more likely to occur when there are large differences of opinion among investors. The latter finding fits with a number of theories, most notably Blanchard and Watson’s (1982) rendition of stockprice bubbles. Analogous results also obtain when we attempt to forecast the skewness of the aggregate stock market, though our statistical power in this case is limited.