Extraction of market expectations from risk-neutral density

Arnerić, Josip; Aljinović, Zdravka; Poklepović, Tea

doi:10.18045/zbefri.2015.2.235

Cited by 3 publications

(4 citation statements)

References 25 publications

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“…A graphical and analytical comparison is presented for each maturity date. The study that is most similar to our research compares three parametric density functions obtained by a mixture of two log-normal (MLN), Black-Scholes-Merton (BSM) and generalized beta (GB2) according to Arnerić et al (2015). Mean square error (MSE) and absolute relative error (ARE) were used for pairwise comparison purpose only, neglecting the "true" probability density function that can be observed ex-post.…”

Section: Research Resultsmentioning

confidence: 99%

Predictive accuracy of option pricing models considering high-frequency data

Arnerić

Marija

2021

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Purpose: Recently, considerable attention has been given to forecasting, not only the mean and the variance, but also the entire probability density function (pdf) of the underlying asset. These forecasts can be obtained as implied moments of future distribution originating from European call and put options. However, the predictive accuracy of option pricing models is not so well established. With this in mind, this research aims to identify the model that predicts the entire pdf most accurately when compared to the ex-post “true” density given by high-frequency data at expiration date. Methodology: The methodological part includes two steps. In the first step, several probability density functions are estimated using different option pricing models, considering the values of major market indices with different maturities. These implied probability density functions are risk neutral. In the second step, the implied pdfs are compared against the “true” density obtained from the high-frequency data to examine which one gives the best fit out-of-sample. Results: The results support the idea that a “true” density function, although unknown, can be estimated by employing the kernel estimator within high-frequency data and adjusted for risk preferences. Conclusion: The main conclusion is that the Shimko model outperforms the Mixture Log-Normal model as well as the Edgeworth expansion model in terms of out-of-sample forecasting accuracy. This study contributes to the existing body of research by: i) establishing the benchmark of the “true” density function using high-frequency data, ii) determining the predictive accuracy of the option pricing models and iii) providing applicative results both for market participants and public authorities.

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Section: Research Resultsmentioning

confidence: 99%

Predictive accuracy of option pricing models considering high-frequency data

Arnerić

Marija

2021

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“…Finally, we can model directly the risk-neutral probability density (RND). Many papers use the double lognormal mixture of Bahra (Bahra 2007;Arneric et al 2015) to represent the RND. The double lognormal mixture is not flexible enough to capture our example of short-maturity smile (Fig.…”

Section: A Short Review Of Implied Volatility Interpolationsmentioning

confidence: 99%

Model-free stochastic collocation for an arbitrage-free implied volatility: Part I

Floc'h

Oosterlee

2019

Decisions Econ Finan

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This paper explains how to calibrate a stochastic collocation polynomial against market option prices directly. The method is first applied to the interpolation of short-maturity equity option prices in a fully arbitrage-free manner and then to the joint calibration of the constant maturity swap convexity adjustments with the interest rate swaptions smile. To conclude, we explore some limitations of the stochastic collocation technique.

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“…Throughout the recent literature, there are papers using semiparametric and nonparametric approaches for estimating implied probability distribution (Breeden & Litzenberger, 2014;Datta, Londono, & Ross, 2017;Malz, 2014;Smith, 2012;Tavin, 2011), some of them are comparing parametric and nonparametric approaches (Aparicio & Hodges, 1998;Mizrach, 2010;Xiao & Zhou, 2017), while several are dealing with parametric (Arneri c et al, 2015;Cheng, 2010;Gemmill & Saflekos, 2000;Grith & Kr€ atschmer, 2011;Khrapov, 2014;S€ oderlind, 2000;V€ ah€ amaa, 2005) or nonparametric approaches only (Andersen & Wagener, 2002;Bahaludin & Abdullah, 2017;Figlewski, 2009;Grith, H€ ardle, & Schienle, 2011;Jackwerth & Rubinstein, 1996). There are only few papers that compare various non-structural models for implied probability distribution estimation (Bliss & Panigirtzoglou, 2002;Coutant et al, 2001;Gemmill & Saflekos, 2000;Jackwerth, 1999;Jondeau et al, 2007;Jondeau & Rockinger, 2000;Santos & Guerra, 2015).…”

Section: Literature Reviewmentioning

confidence: 99%

“…This way the out-ofsample performances of the three non-structural models are compared using MSE and DM test. Comparison of the first moments of the distribution and the spot prices at the expiration date of the option, i.e., the forecasting performances, is performed in only few papers (Arneri c et al, 2015;Bahaludin & Abdullah, 2017;Benavides & Mora, 2008), while forecasting accuracy via updated mean and variance on the next trading day is given only in Gemmil and Saflekos (2000). Therefore, literature lacks papers that compare RNDs for forecasting purposes in general and especially for comparison of different non-structural approaches and for different maturity horizons.…”

Section: Literature Reviewmentioning

confidence: 99%

Non-structural approach to implied moments extraction

Šestanović

Arnerić

Aljinović

2018

Economic Research-Ekonomska Istraživanja

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Moments of future prices and returns are not observable, but it is possible to measure them indirectly. A set of option prices with the same maturity but with different exercise prices are used to extract implied probability distribution of the underlying asset at the expiration date. The aim is to obtain market expectations from options and to investigate which non-structural model for estimating implied probability distribution gives the best fit. Nonstructural models assume that only dynamics in prices is known. Mixture of two log-normals (MLN), Edgeworth expansions and Shimko's model (representatives of parametric, semiparametric and nonparametric approaches respectively) are compared. Previous researches are inconclusive about the superiority of one approach over the others. This article contributes to finding which approach dominates. The best fit model is used to describe moments of the implied probability distribution. The sample covers one-year data for DAX index options. The results are compared through models and maturities. All models give better short-term forecasts. In pairwise comparison, MLN is superior to other approaches according to mean squared errors and Diebold-Mariano test in the observed period for DAX index options.

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Extraction of market expectations from risk-neutral density

Abstract: The purpose of this paper is to investigate which of the proposed parametric models for extracting risk-neutral

Cited by 3 publications

References 25 publications

Predictive accuracy of option pricing models considering high-frequency data

Predictive accuracy of option pricing models considering high-frequency data

Model-free stochastic collocation for an arbitrage-free implied volatility: Part I

Non-structural approach to implied moments extraction

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