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445
Nonparametric Estimation of StatePrice Densities Implicit In Financial Asset Prices
 JOURNAL OF FINANCE
, 1997
"... Implicit in the prices of traded financial assets are ArrowDebreu prices or, with continuous states, the stateprice density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitragefree metho ..."
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Cited by 339 (6 self)
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Implicit in the prices of traded financial assets are ArrowDebreu prices or, with continuous states, the stateprice density (SPD). We construct a nonparametric estimator for the SPD implicit in option prices and derive its asymptotic sampling theory. This estimator provides an arbitragefree method of pricing new, complex, or illiquid securities while capturing those features of the data that are most relevant from an assetpricing perspective, e.g., negative skewness and excess kurtosis for asset returns, volatility "smiles" for option prices. We perform Monte Carlo experiments and extract the SPD from actual S&P 500 option prices.
Post'87 Crash Fears in the S&P 500 Futures Option Market
, 1998
"... Postcrash distributions inferred from S ..."
Implied Volatility Functions: Empirical Tests
, 1995
"... Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violat ..."
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Cited by 303 (4 self)
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Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time. Since the volatility function in their model has an arbitrary specification, the deterministic volatility (DV) option valuation model has the potential of fitting the observed crosssection of option prices exactly. Using a sample of S&P 500 index options during the period June 1988 and December 1993, we attempt to evaluate the economic significance of the implied volatility function by examining the predictive and hedging performance of the DV option valuation model. Discussion draft: September 8, 1995 ____________________________________________...
A JumpDiffusion Model for Option Pricing
 Management Science
, 2002
"... Brownian motion and normal distribution have been widely used in the Black–Scholes optionpricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (as ..."
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Cited by 237 (9 self)
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Brownian motion and normal distribution have been widely used in the Black–Scholes optionpricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called “volatility smile ” in option markets. To incorporate both of them and to strike a balance between reality and tractability, this paper proposes, for the purpose of option pricing, a double exponential jumpdiffusion model. In particular, the model is simple enough to produce analytical solutions for a variety of optionpricing problems, including call and put options, interest rate derivatives, and pathdependent options. Equilibrium analysis and a psychological interpretation of the model are also presented.
Pricing And Hedging Derivative Securities In Markets With Uncertain Volatilities
 Applied Mathematical Finance
, 1995
"... We present a model for pricing and hedging derivative securities and option portfolios in an environment where the volatility is not known precisely, but is assumed instead to lie between two extreme values oe min and oe max . These bounds could be inferred from extreme values of the implied volatil ..."
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Cited by 165 (3 self)
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We present a model for pricing and hedging derivative securities and option portfolios in an environment where the volatility is not known precisely, but is assumed instead to lie between two extreme values oe min and oe max . These bounds could be inferred from extreme values of the implied volatilities of liquid options, or from highlow peaks in historical stock or optionimplied volatilities. They can be viewed as defining a confidence interval for future volatility values. We show that the extremal nonarbitrageable prices for the derivative asset which arise as the volatility paths vary in such a band can be described by a nonlinear PDE, which we call the BlackScholesBarenblatt equation. In this equation, the "pricing" volatility is selected dynamically from the two extreme values oe min ,oe max , according to the convexity of the valuefunction. A simple algorithm for solving the equation by finitedifferencing or a trinomial tree is presented. We show that this model capture...
Does net buying pressure affect the shape of implied volatility functions
 Journal of Finance
, 2004
"... This paper examines the relation between net buying pressure and the shape of the implied volatility function (IVF) for index and individual stock options. We find that changes in implied volatility are directly related to net buying pressure from public order flow. We also find that changes in impl ..."
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Cited by 146 (3 self)
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This paper examines the relation between net buying pressure and the shape of the implied volatility function (IVF) for index and individual stock options. We find that changes in implied volatility are directly related to net buying pressure from public order flow. We also find that changes in implied volatility of S&P 500 options are most strongly affected by buying pressure for index puts, while changes in implied volatility of stock options are dominated by call option demand. Simulated deltaneutral optionwriting trading strategies generate abnormal returns that match the deviations of the IVFs above realized historical return volatilities. If people are willing to pay foolish prices for insurance, why shouldn’t we sell it to them? (Lowenstein (2000)). ONE OF THE MOST INTRIGUING ANOMALIES REPORTED in the derivatives literature is the “implied volatility smile. ” The name arose from the fact that, prior to the October 1987 market crash, the relation between the Black and Scholes (1973) implied volatility of S&P 500 index options and exercise price gave the ap
New Insights Into Smile, Mispricing and Value At Risk: The Hyperbolic Model
 Journal of Business
, 1998
"... We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black ..."
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Cited by 136 (7 self)
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We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical BlackScholes model. We study implicit volatilities, the smile effect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit riskneutral density function from option data. Finally we present some new valueat risk calculations leading to new perspectives to cope with model risk. I Introduction There is little doubt that the BlackScholes model has become the standard in the finance industry and is applied on a large scale in everyday trading operations. On the other side its deficiencies have become a standard topic in research. Given the vast literature where refinements a...
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 113 (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.
JumpDi®usion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing
 Review of Derivatives Research
, 2000
"... Abstract. This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (Parti ..."
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Cited by 99 (3 self)
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Abstract. This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (Partial IntegroDifferential Equation) and demonstrates how this equation can be used to fit the model to European option prices. For numerical pricing of general contingent claims, we develop an ADI finite difference method that is shown to be unconditionally stable and, if combined with Fast Fourier Transform methods, computationally efficient. The paper contains several detailed examples from the S&P500 market.