Retrieving Risk Neutral Moments from Option Prices

Rompolis, Leonidas S.; Tzavalis, Elias

doi:10.2139/ssrn.936670

Cited by 6 publications

(9 citation statements)

References 47 publications

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“…2 Note that the formulas appeared in footnote 1 can be generalized to retrieve risk neutral moments of more complicated random variables using generic European-style options, such as Asian or basket (see Rompolis and Tzavalis, 2009). They can also be applied to American option prices after adjusting for the early exercise premium (see Melick and Thomas, 1997).…”

Section: Maximum Entropy Density Implied By Option Pricesmentioning

confidence: 99%

Retrieving risk neutral densities from European option prices based on the principle of maximum entropy

Rompolis

2010

Journal of Empirical Finance

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Section: Maximum Entropy Density Implied By Option Pricesmentioning

confidence: 99%

Retrieving risk neutral densities from European option prices based on the principle of maximum entropy

Rompolis

2010

Journal of Empirical Finance

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“…. Estimates of μ X,n can be directly obtained from out-of-the-money (OTM) European call and put prices employing the formulas of the risk neutral moments (RNM) suggested by Bakshi, Kapadia and Madan (2003) for n = 1, 2, 3, and 4 and, recently, extended by Rompolis and Tzavalis (2004) to any order n as…”

Section: The C-type Gcsementioning

confidence: 99%

Recovering Risk Neutral Densities from Option Prices: A New Approach

Rompolis

Tzavalis

2008

J. Financ. Quant. Anal.

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In this paper we present a new method of approximating the risk neutral density (RND) from option prices based on the C-type Gram-Charlier series expansion (GCSE) of a probability density function. The exponential form of this type of GCSE guarantees that it will always give positive values of the risk neutral probabilities, and it can allow for stronger deviations from normality, which are two drawbacks of the A-type GCSE used in practice. To evaluate the performance of the suggested expansion of the RND, the paper presents simulation and empirical evidence.

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“…In Corollary 1 of their paper they derive the Breeden and Litzenberger (1978) result from their Proposition 1, which itself is a corollary of Theorem 1 of Bakshi and Madan (2000). Proposition 2 of Rompolis and Tzavalis (2004) and its Corollaries 2 and 3, provide general analytical formulae for conditional asset return moments of order m, where m = 1, and m ≥ 2. These are reproduced here as equations ( 9) and ( 10) below.…”

Section: 'Model Free' Implied Moments: Literature Reviewmentioning

confidence: 98%

“…These are reproduced here as equations ( 9) and ( 10) below. The Rompolis and Tzavalis (2004) formula are 6 :…”

Section: 'Model Free' Implied Moments: Literature Reviewmentioning

confidence: 99%

Test of recent advances in extracting information from option prices

Healy

Gregoriou

Hudson

2018

International Review of Financial Analysis

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A large literature exists on techniques for extracting probability distributions for future asset prices from option prices. No definitive method has been developed however. The parametric ‘mixture of normals’, and nonparametric ‘smoothed implied volatility’ methods remain the most widespread approaches. These though are subject to estimation errors due to discretization, truncation, and noise. Recently, several authors have derived ‘model free’ formulae for computing the moments of the risk neutral density (RND) directly from option prices, without first estimating the full density. The accuracy of these formulae is studied here for the first time. The Black-Scholes formula is used to generate option prices, and error curves for the first 4 moments of the RND are computed using the ‘model-free’ formulae. It is found that, in practice, the formulae are prone to large and economically significant errors, because they contain definite integrals that can only be solved numerically. We show that without mathematically equivalent expressions with analytical solutions the formulae are difficult to deploy effectively in practice

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Retrieving Risk Neutral Moments from Option Prices

Cited by 6 publications

References 47 publications

Retrieving risk neutral densities from European option prices based on the principle of maximum entropy

Retrieving risk neutral densities from European option prices based on the principle of maximum entropy

Recovering Risk Neutral Densities from Option Prices: A New Approach

Test of recent advances in extracting information from option prices

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