# Risk-Neutral Densities: A Review

@article{Figlewski2018RiskNeutralDA, title={Risk-Neutral Densities: A Review}, author={Stephen Figlewski}, journal={Annual Review of Financial Economics}, year={2018} }

Trading in options with a wide range of exercise prices and a single maturity allows a researcher to extract the market's risk-neutral density (RND) over the underlying price at expiration. The RND contains investors’ beliefs about the true probabilities blended with their risk preferences, both of which are of great interest to academics and practitioners alike. With a particular focus on US equity options, I review the historical development of this powerful concept, practical details of…

## 36 Citations

The Second Partial Derivative of Option Price with Respect to the Strike: A Historical Reminiscence

- Economics
- 2018

An option’s market price reflects the risk-neutral probability that it will end up in the money. Research has been increasing in recent years that shows how, given a set of market prices for options…

A new representation of the risk-neutral distribution and its applications

- EconomicsQuantitative Finance
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This paper establishes a novel model-free representation of the risk-neutral density in terms of market-observed options prices by combining exact series representations of the Dirac Delta function…

The Ex Ante Physical Distributions of Individual Stock Returns

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I present a method for deriving the entire physical return distributions of individual stocks directly from option prices. The method is theoretically nested in an equilibrium model, obeys the law-of…

On the RND under Heston's Stochastic Volatility Model

- Mathematics
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We consider Heston's (1993) stochastic volatility model for valuation of European options to which (semi) closed form solutions are available and are given in terms of characteristic functions. We…

Option-Implied Dependence and Correlation Risk Premium

- Economics
- 2020

We propose a novel model-free approach to obtain the joint risk-neutral distribution among several assets that is consistent with options on these assets and their weighted index. We implement this…

Distorting Arrow-Debreu Securities: New Entropy Restrictions Implied by the Option Cross Section

- Economics
- 2020

Replacing equity return (as in the equity risk premium) with returns on an arbitrary contingent claim, we obtain a new class of economic risk premiums to impose upon candidate models. These risk…

Risk-Neutral Density Estimation: Looking at the Tails

- EconomicsThe Journal of Derivatives
- 2019

Previous estimation results of risk-neutral densities explain in rather general terms that the tails of the resulting distribution “look fat,” and a way has to be found to model the tails of the…

A Model-Free Fourier Cosine Method for Estimating the Risk-Neutral Density

- Computer ScienceThe Journal of Derivatives
- 2021

A new model-free method to extract the risk-neutral density from market-observed options prices based on novelly combining the Fourier cosine series method and the Carr-Madan spanning formula is presented.

Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions

- EconomicsJournal of Futures Markets
- 2019

This article compares several widely used and recently developed methods to extract risk‐neutral densities (RNDs) from option prices in terms of estimation accuracy. It shows that the positive…

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