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Of Smiles and Smirks: A TermStructure Perspective
 JOURNAL OF FINANCIAL AND QUANTITATIVE ANALYSIS
, 1998
"... An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts i ..."
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Cited by 79 (3 self)
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An extensive empirical literature in finance has documented not only the presence of anamolies in the BlackScholes model, but also the "termstructures" of these anamolies (for instance, the behavior of the volatility smile or of unconditional returns at different maturities). Theoretical efforts in the literature at addressing these anamolies have largely focussed on two extensions of the BlackScholes model: introducing jumps into the return process, and allowing volatility to be stochastic. This paper employs commonlyused versions of these two classes of models to examine the extent to which the models are theoretically capable of resolving the observed anamolies. We find that each model exhibits some "termstructure" patterns that are fundamentally inconsistent with those observed in the data. As a consequence, neither class of models constitutes an adequate explanation of the empirical evidence, although stochastic volatility models fare better than jumps in this regard.
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 51 (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 price of a smile. Hedging and spanning in option markets
 Review of Financial Studies
, 2001
"... i Abstract: The volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed in order to accommodate that change. Deterministic volatility models allow for more °exible volatility surfaces but refrain from introducing additional riskfactors. Thus, o ..."
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Cited by 19 (1 self)
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i Abstract: The volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed in order to accommodate that change. Deterministic volatility models allow for more °exible volatility surfaces but refrain from introducing additional riskfactors. Thus, options are still redundant securities. Alternatively, stochastic models introduce additional riskfactors and options are then needed for spanning of the pricing kernel. We develop a statistical test based on this di®erence in spanning. Using daily S&P500 index options data from 19861995, our tests suggest that both in and outofthemoney options are needed for spanning. The ¯ndings are inconsistent with deterministic volatility models but are consistent with stochastic models which incorporate additional priced riskfactors such as stochastic volatility, interest rates, or jumps. What is a good model to price equity derivatives and to manage risk? Starting from Black and Scholes (1973), a common approach in the derivative pricing literature has been to model the underlying asset as a geometric Brownian motion with constant volatility. Early tests of options on stocks such as Rubinstein (1985) more or less supported the empirical implications of a geometric
2001), The Pricing Kernel Puzzle: Reconciling Index Option Data and Economic Theory, Working Paper
"... One of the central questions in financial economics is the determination of asset prices, such as the value of a stock. Over the past three decades, research on this topic has converged on a concept called the “stateprice density”. However, a puzzle has arisen. On the one hand, Cox, Ingersoll, and ..."
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Cited by 16 (0 self)
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One of the central questions in financial economics is the determination of asset prices, such as the value of a stock. Over the past three decades, research on this topic has converged on a concept called the “stateprice density”. However, a puzzle has arisen. On the one hand, Cox, Ingersoll, and Ross (1985) and others argue that the ratio of the stateprice density to the statistical probability density, which is commonly known as the pricing kernel, should decrease monotonically as the aggregate wealth of an economy rises. On the other hand, recent empirical work on options on the S&P 500 index suggests that, for a sizable range of index levels, the pricing kernel is increasing instead of decreasing. We investigate theoretical explanations to this puzzle. Our existing work has ruled out some alternative hypotheses, such as data imperfections and methodological problems. The current paper focuses on the hypothesis of statedependent utility. Statedependent utility can arise from diverse causes such as habit persistence, stochastic index volatility, or dependence on interest rates or other asset prices. In this paper we characterize a general relation between the index and the state variables that is required to explain the puzzle. However, it remains for us to provide economic reasoning to justify this relation. The existing literature is largely unsatisfactory with respect to this puzzle, and most research does not touch on the puzzle altogether.
Pricing options on scalar diffusions: an eigenfunction expansion approach
 Management Science
"... This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing ..."
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Cited by 10 (5 self)
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This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications: pricing vanilla, single and doublebarrier options under the constant elasticity of variance (CEV) process and interest rate knockout options in the CoxIngersollRoss (CIR) termstructure model.
IMPLIED AND LOCAL VOLATILITIES UNDER STOCHASTIC VOLATILITY
, 2001
"... For asset prices that follow stochasticvolatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process. We also give app ..."
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Cited by 10 (3 self)
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For asset prices that follow stochasticvolatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process. We also give applications, including riskpremiumbased explanations of the biases in some naïve pricing and hedging schemes. We begin by reviewing option pricing under stochastic volatility and representing option prices and local volatilities in terms of expectations. In the case that fluctuations in price and volatility have zero correlation, the expectations formula shows that local volatility (like implied volatility) as a function of logmoneyness has the shape of a symmetric smile. In the case of nonzero correlation, we extend Sircar and Papanicolaou’s asymptotic expansion of implied volatilities under slowlyvarying stochastic volatility. An asymptotic expansion of local volatilities then verifies the rule of thumb that local volatility has the shape of a skew with roughly twice the slope of the implied volatility skew. Also we compare the slowvariation asymptotics against what we call smallvariation asymptotics, and against Fouque, Papanicolaou, and Sircar’s rapidvariation
u 1 Recovering Probabilities from Option Prices d C=f(S,t) Recovering Probabilities and Risk Aversion from Options Prices and Realized Returns
, 1997
"... papers may be downloaded at: ..."
Volatility Forecasts of the S&P100 by Evolutionary Programming in a Modified Time Series Data Mining Framework
"... Traditional parametric methods have limited success in estimating and forecasting the volatility of financial securities. Recent advance in evolutionary computation has provided additional tools to conduct data mining effectively. The current work applies the genetic programming in a Time Series Dat ..."
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Traditional parametric methods have limited success in estimating and forecasting the volatility of financial securities. Recent advance in evolutionary computation has provided additional tools to conduct data mining effectively. The current work applies the genetic programming in a Time Series Data Mining framework to characterize the S&P100 high frequency data in order to forecast the one step ahead integrated volatility. Results of the experiment have shown to be superior to those derived by the traditional methods.