Risk-Neutral Densities: A Review

@article{Figlewski2018RiskNeutralDA,
  title={Risk-Neutral Densities: A Review},
  author={Stephen Figlewski},
  journal={Annual Review of Financial Economics},
  year={2018}
}
  • Stephen Figlewski
  • Published 1 November 2018
  • Economics
  • Annual Review of Financial Economics
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… 
The Second Partial Derivative of Option Price with Respect to the Strike: A Historical Reminiscence
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
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
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
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
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
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
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
TLDR
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
  • Shan Lu
  • Economics
    Journal 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
...
...

References

SHOWING 1-10 OF 80 REFERENCES
Estimating the Implied Risk Neutral Density
The market's risk neutral probability distribution for the value of an asset on a future date can be extracted from the prices of a set of options that mature on that date, but two key technical
Volatility Risk Premiums Embedded in Individual Equity Options
The accumulation of trading experience and empirical evidence since the original Black-Scholes (BS) model was developed, have made it increasingly evident that volatility is not a constant parameter,
Option-Implied Risk-Neutral Distributions and Risk Aversion
Analysts are accustomed to using prices for the information they contain. A stock price, for example, can be thought of as an expected value of future cash flows. Each futures price and option price
Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review
TLDR
This selective literature review starts by observing that in efficient markets, there is information incorporated in option prices that might help to design option pricing models, and moves beyond one time to expiration to the construction of implied binomial trees, which model the stochastic process of the underlying asset.
Empirical Performance of Alternative Option Pricing Models
Substantial progress has been made in extending the Black-Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps.On the empirical front, however, it
Option-Implied Risk Aversion Estimates
Using a utility function to adjust the risk-neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options,
The pricing kernel puzzle: survey and outlook
It has been a while since the literature on the pricing kernel puzzle was summarized in Jackwerth (Option-implied risk-neutral distributions and risk-aversion, The Research Foundation of AIMR,
The pricing of convexity risk and timedecay in options markets
Anatomy of a Meltdown: The Risk Neutral Density for the S&P 500 in the Fall of 2008
We examine the risk neutral probability density (RND) for the S&P 500 extracted from real-time bid and ask quotes for index options, under extreme market stress during the fall of 2008. The RND
Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application
In this paper, we examine the pricing of European call options on stocks that have variance rates that change randomly. We study continuous time diffusion processes for the stock return and the
...
...