Probability Weighting and Asset Prices

Dierkes, Maik

doi:10.2139/ssrn.2253817

Cited by 12 publications

(8 citation statements)

References 54 publications

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“…Here we allow the weighting function

w

to depend explicitly on time

t

. This is not just for mathematical generality; the time variation of probability weighting is supported empirically (Cui et al., 2020; Dierkes, 2013).…”

Section: Problem Formulationmentioning

confidence: 99%

Consistent investment of sophisticated rank‐dependent utility agents in continuous time

Jin

2021

Mathematical Finance

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We study portfolio selection in a complete continuous‐time market where the preference is dictated by the rank‐dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of a sophisticated consistent planners who seek (subgame perfect) intra‐personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than one corresponding to an effective reduction in risk premium due to probability weighting.

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“…Here we allow the weighting function

w

to depend explicitly on time

t

. This is not just for mathematical generality; the time variation of probability weighting is supported empirically (Cui et al., 2020; Dierkes, 2013).…”

Section: Problem Formulationmentioning

confidence: 99%

Consistent investment of sophisticated rank‐dependent utility agents in continuous time

Jin

2021

Mathematical Finance

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“…That allows the utility function to be the same for all maturities but the weighting function scales with maturity. Empirically, Dierkes (2013) then finds the weighting function to be inverse-Sshaped and the utility function to be convex-concave around the zero percent return.…”

Section: Models With Probability Weighting Functionsmentioning

confidence: 99%

The Pricing Kernel Puzzle: Survey and Outlook

Cuesdeanu

Jackwerth

2016

SSRN Journal

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“…All of the above can be characterized by "probability judgment error" 2 (see e.g. Dierkes et al, 2020;Baele et al, 2019;He and Zhou, 2016;Kuhnen, 2015;Wigniolle, 2014;Polkovnichenko and Zhao, 2013;Dierkes, 2013;Chabi-Yo and Song, 2013;Kliger and Levy, 2010;Dierkes, 2009;Ackert et al, 2009;Haigh and List, 2005;Kluger and Wyatt, 2004;Fox et al, 1996). Psychological probability, by and through the probability weighting function component of rank dependent utility and prospect theory (Quiggin, 1982(Quiggin, , 1993Lopes, 1987Lopes, , 1990Tversky and Kahneman, 1992), plays a key role in evaluating probability judgment error in many of those papers.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Chabi-Yo and Song (2013) established a nexus between VIX scores and pwfs by showing how to recover pwfs nonparametrically from S&P 500 index option implied volatility and VIX options. Dierkes (2013) also provides a link between VIX and the curvature of source functions.…”

Section: Introductionmentioning

confidence: 99%

Market Instability, Investor Sentiment, and Probability Judgment Error in Index Option Prices

Charles-Cadogan

2021

SSRN Journal

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In a natural experiment with index option prices, we study how probability judgment error, and probabilistic risk attitudes, characterize investors' sentiment about the ranking of index option attractiveness, the weight they place on each rank, and their ability to discriminate between prices. We introduce a novel behavioral process that (1) characterizes investor sentiment about tail events in index option prices over time and probability ranks, (2) provides early warning signals of market instability, and (3) crash probability estimates from a closed form expression for the time varying transition probability that a seemingly stable market state will become unstable and crash.

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Probability Weighting and Asset Prices

Cited by 12 publications

References 54 publications

Consistent investment of sophisticated rank‐dependent utility agents in continuous time

Consistent investment of sophisticated rank‐dependent utility agents in continuous time

The Pricing Kernel Puzzle: Survey and Outlook

Market Instability, Investor Sentiment, and Probability Judgment Error in Index Option Prices

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