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

Rompolis, Leonidas S.

doi:10.1016/j.jempfin.2010.04.007

Cited by 34 publications

(24 citation statements)

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“…Monteiro and Vecentec [28] presented a new approach for estimating RND achieved in the space of cubic splines ensuring positivity for the polynomial functions. Rompolis [29] suggested a new method of using the principle of entropy maximization. Figlewski [9] combined smoothing techniques to reflect the bid-ask spread and a new method of completing the density with tails from a generalized extreme value distribution.…”

Section: Risk Neutral Densitymentioning

confidence: 99%

The Implied Risk Neutral Density Dynamics: Evidence from the S&P TSX 60 Index

Souissi

2017

Journal of Applied Mathematics

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The risk neutral density is an important tool for analyzing the dynamics of financial markets and traders' attitudes and reactions to already experienced shocks by financial markets as well as the potential ones. In this paper, we present a new method for the extraction information content from option prices. By eliminating bias caused by daily variation of contract maturity through a completely nonparametric technique based on kernel regression, we allow comparing evolution of risk neutral density and extracting from time continuous indicators that detect evolution of traders' attitudes, risk perception, and belief homogeneity. This method is useful to develop trading strategies and monetary policies.

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Section: Risk Neutral Densitymentioning

confidence: 99%

The Implied Risk Neutral Density Dynamics: Evidence from the S&P TSX 60 Index

Souissi

2017

Journal of Applied Mathematics

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“…This can be straighforwardly done based on a probability density function estimation method relying on knowledge of the moments of this density. The method (principle) of maximum entropy constitutes a natural choice for this exercise (Stutzer 1996;Rockinger and Jondeau 2002;Rompolis 2010, for financial applications of this method). This method exploits a number of moment conditions up to order M in deriving a probability density function.…”

Section: Rndmentioning

confidence: 99%

“…Secondly, they can be employed to examine the relationship between higher-order risk neutral moments of asset returns and their physical counterparts, and/or to estimate the implied risk aversion coefficient of the stock and option markets participants (Bakshi et al 2003;Bakshi and Madan 2006a, b;Rompolis and Tzavalis 2010;Polkovnichenko and Zhao 2013). Thirdly, they can be applied to estimate the risk neutral density (RND) of the underlying asset return based on an approximation density method (Corrado and Su 1996;Ang et al 2002;Rompolis and Tzavalis 2008;Rompolis 2010;Mozumder et al 2013;Ghysels and Wang 2014). This density can be in turn employed to price option contacts in a model-free manner.…”

Section: Introductionmentioning

confidence: 99%

Retrieving risk neutral moments and expected quadratic variation from option prices

Rompolis

Tzavalis

2016

Rev Quant Finan Acc

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This paper derives exact formulas for retrieving risk neutral moments of future payoffs of any order from generic European-style option prices. It also provides an exact formula for retrieving the expected quadratic variation of the stock market implied by European option prices, which nowadays is used as an estimate of the implied volatility, and a formula approximating the jump component of this measure of variation. To implement the above formulas to discrete sets of option prices, the paper suggests a numerical procedure and provides upper bounds of its approximation errors. The performance of this procedure is evaluated through a simulation and an empirical exercise. Both of these exercises clearly indicate that the suggested numerical procedure can provide accurate estimates of the risk neutral moments, over different horizons ahead. These can be in turn employed to obtain accurate estimates of risk neutral densities and calculate option prices, efficiently, in a model-free manner. The paper also shows that, in contrast to the prevailing view, ignoring the jump component of the underlying asset can lead to seriously biased estimates of the new volatility index suggested by the Chicago Board Options Exchange.

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“…The principle of maximum entropy is a natural candidate for this exercise (see Stutzer (1996), Rockinger and Jondeau (2002) and Rompolis (2010a) for financial applications of this principle).…”

Section: Option Pricing Using the Forecasted Cumulantsmentioning

confidence: 99%