Implied Volatility Skews and Stock Index Skewness and Kurtosis Implied by S&amp;P 500 Index Option Prices

Corrado, Charles J.; Su, Tie

doi:10.3905/jod.1997.407978

Cited by 115 publications

(58 citation statements)

References 9 publications

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“…Lévy processes [7,8,9,10], stochastic volatility models [11,12,13,6,14,15] or cumulant expansions around the Black-Scholes case [16,17,18,19,10] constitute approaches which have been successful in capturing some of the features of real option prices. For example the recent 'stochastic alpha, beta, rho' (SABR) model ( [6], and see Appendix C) can be well-fit to empirical skew surfaces.…”

Section: Introductionmentioning

confidence: 99%

A non-Gaussian option pricing model with skew

Borland¹,

Bouchaud²

2004

RQUF

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Closed form option pricing formulae explaining skew and smile are obtained within a parsimonious non-Gaussian framework. We extend the non-Gaussian option pricing model of L. Borland (Quantitative Finance, 2, 415-431, 2002) to include volatility-stock correlations consistent with the leverage effect. A generalized Black-Scholes partial differential equation for this model is obtained, together with closedform approximate solutions for the fair price of a European call option. In certain limits, the standard Black-Scholes model is recovered, as is the Constant Elasticity of Variance (CEV) model of Cox and Ross. Alternative methods of solution to that model are thereby also discussed. The model parameters are partially fit from empirical observations of the distribution of the underlying. The option pricing model then predicts European call prices which fit well to empirical market data over several maturities.

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Section: Introductionmentioning

confidence: 99%

A non-Gaussian option pricing model with skew

Borland¹,

Bouchaud²

2004

RQUF

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“…e.g. [9], [24] and [25]) shows that the implied skewness of the underlying used in options is often negative, in contrary to the skewness of log-normal distributions. In order to take into account negative skewness Savickas proposed to use Weibull distributions (cf.…”

Section: Estimation Using Log-normal Mixturesmentioning

confidence: 99%

Parametric Estimation of Risk Neutral Density Functions

Grith

Krätschmer

2011

Handbook of Computational Finance

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Summary. This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions determining the risk neutral distributions. We we shall differentiate between the direct and the indirect way. Following the direct way, parameter vectors are estimated which characterize the distributions from selected statistical families to model the risk neutral distributions. The idea of the indirect approach is to calibrate characteristic parameter vectors for stochastic models of the asset price processes, and then to extract the risk neutral density function via Fourier methods. For every of the reviewed methods the calculation of option prices under hypothetically true risk neutral distributions is a building block. We shall give explicit formula for call and put prices w.r.t. reviewed parametric statistical families used for direct estimation. Additionally, we shall introduce the Fast Fourier Transform method of call option pricing developed in [6]. It is intended to compare the reviewed estimation methods empirically.

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“…Using the same polynomials but with restrictions on some of the coefficients, Jondeau and Rockinger [1998a] and Corrado and Su [1997] restrict their attention to the class of Gram-Charlier expansions. Jondeau and Rockinger [1998a] also provide an algorithm that forces the coefficients, which are based on the moments of the risk-neutral distribution, to lie within the region that guarantees positive probabilities.…”

Section: Parametric Methodsmentioning

confidence: 99%

“…As a main benefit, the authors note that the approximated risk-neutral distribution has unbiased moments. Jarrow and Rudd [1982], Corrado and Su [1996], Longstaff [1995], and Rubinstein [1998] use Edgeworth expansions. Here, the base distribution (lognormal, lognormal, normal, and binomial, respectively) is augmented with correction terms that successively match each of the first four cumulants.…”

Section: Parametric Methodsmentioning

confidence: 99%