Risk-adjusted option-implied moments

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may Risk-Adjusted Option-Implied Moments AbstractOption-implied moments, like implied volatility, contain useful information about an underlying asset's return distribution, but are derived under the risk-neutral probability measure. This paper shows how to convert risk-neutral moments into the corresponding physical ones. The main theoretical result expresses moments under the physical probability measure in terms of observed option prices and the preferences of a representative investor. Based on this result, we investigate several empirical questions. We show that a model of a representative investor with CRRA utility can explain the variance risk premium for the S&P500 index but fails to capture variance and skewness risk premiums simultaneously. Moreover, we present methods to estimate forward-looking market risk premiums and investors' disappointment aversion implied in market prices. JEL Classification: G13, G17, C51, C53 1 I IntroductionThe use of option prices to gain information about the underlying's return distribution is an important idea in finance. Certainly, the most prominent example is implied volatility that goes back to Latané and Rendleman (1976) Option-implied moments have the drawback that they are formed under the riskneutral probability measure, whereas many applications require moments under the physical (real-world, actual, subjective) probability measure. Ideally, one would exploit all information contained in current option prices and have a simple but economically justified method to adjust for risk, i.e., to move from the risk-neutral moment to the corresponding physical moment. This paper provides such a method by showing explicitly how the risk adjustment depends on current option prices and risk preferences. This result has many potential uses. A specific one is to express ex-ante return moments under the physical measure, which we call risk-adjusted implied moments, in terms of observed option prices and preferences. The presented methodology 2 is very general. It applies to implied moments as in Neuberger (2012), implied moments as in Bakshi, Kapadia, and Madan (2003), which refer to log returns, and to the corresponding moments of discrete returns. It can deal with both central and non-central moments and is not restricted to a narrow class of utility functions.The empirical contributions of the paper refer to different applications of the presented methodology for the S&P500 index....

Analysis of option returns in perfect and imperfect markets

“…This paper studied the option-implied risk-adjusted approach by Brinkmann and Korn (2018) in predicting mean realized S&P500 index option returns in perfect markets. The approach extracts the option-implied expectations of a representative investor with riskaverse utility to capture the wedge between the risk-neutral and physical measure.…”

“…When option market prices are observable, expected option returns are determined solely by the physical expected option payoff. The option-implied risk-adjusted moments framework derived in Brinkmann and Korn (2018) presents a model-free approach to infer the expected physical payoffs of European contingent claims from current option market prices representing the investor's believe and a utility function (U ) to model investor's taste of risk. The approach is based on the general relationship between the risk-neutral (q) and physical density (p) given by…”

“…The approach is highly flexible as it allows for any risk-averse utility function to capture investor preferences. Compared to other modelfree approaches, moments are obtained without explicit construction of the risk-neutral density, avoiding severe numerical problems (Brinkmann and Korn 2018).…”

“…As shown in Brinkmann and Korn (2018), expected market return can be expressed via at-the-money physical expected option payoffs: index prices over the sample period. One can observe that implied risk aversion after 2001 correlated with the underlying price: when the index reached record highs, investors became more risk-averse and vice versa.…”

“…Chapter 2 applies the approach by Brinkmann and Korn (2018) to explain S&P500 index option returns in perfect markets. This option-implied risk-adjusted approach captures the risk-aversion of a representative investor through a utility function to infer the physical measure from the risk-neutral measure.…”