Pricing rules and Arrow–Debreu ambiguous valuation

Araújo, Aloísio; Chateauneuf, Alain; Faro, José Heleno

doi:10.1007/s00199-011-0660-4

Cited by 27 publications

(21 citation statements)

References 43 publications

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“…Economies with incomplete financial markets are also closely related because the so‐called super‐replication functional is also a Knightian expectation. Araujo, Chateauneuf, and Faro () discussed sublinear functionals that satisfy similar axioms as our Knightian expectation. They showed that the sublinear price functional is equal to the superhedging price of an exogenous incomplete and arbitrage‐free financial market if and only if the subspace of claims whose expectation does not depend on a specific prior

P \in normalℙ

coincides with the subspace of undominated claims under

normal𝔼

.…”

Section: Knight–walras Equilibriummentioning

confidence: 99%

Equilibria Under Knightian Price Uncertainty

Beißner¹,

Riedel²

2019

Econometrica

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We study economies with Knightian uncertainty about state prices. We introduce an equilibrium concept with sublinear prices and prove that equilibria exist under weak conditions. In general, such equilibria lead to inefficient allocations; they coincide with Arrow-Debreu equilibria if and only if the values of net trades are ambiguity-free in mean. In economies without aggregate uncertainty, inefficiencies are generic. Equilibrium allocations under price uncertainty are efficient in a constrained sense that we call uncertainty-neutral efficient. Arrow-Debreu equilibria turn out to be non-robust with respect to the introduction of Knightian uncertainty.

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P \in normalℙ

coincides with the subspace of undominated claims under

normal𝔼

.…”

Section: Knight–walras Equilibriummentioning

confidence: 99%

Equilibria Under Knightian Price Uncertainty

Beißner¹,

Riedel²

2019

Econometrica

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“…In this sense, m > 0 (m < 0) signifies investor optimism (pessimism) and s = 1 means volatility is measured subjectively, generally underestimated, because of behavioral factor s. Since m and s are both determined by the capacity variable c, the latter is usually viewed as a composite indicator of investor ambiguity and uncertainty attitudes. Comparable to k-ignorance, c has been used as a measure of uncertainty attitude or degree of confidence about probabilistic judgment in decision-making and behavioral economics (Eichberger and Kelsey 1999;Wakker 2001;Araujo et al 2012). Acting as a conditional capacity in the Choquet integral, c summarizes decision-makers' ambiguity perceptions about index prices, with 0 < c < 0.5 representing degrees of ambiguity aversion, while 0.5 < c < 1 implying ambiguity-seeking behavior.…”

Section: Background and Modeling Frameworkmentioning

confidence: 99%

“…We extend the Black-Scholes (BS) (1973) setting by incorporating ambiguity through Choquet Brownian motions, multiple-priors and the notion of c-ignorance (see e.g., Chateauneuf et al 1996;Agliardi and Sereno 2011;Araujo et al 2012) to the option pricing apparatus. We then use our extended model to empirically assess the informational efficiency of option implied volatility and ambiguity as predictors of stock index realized volatility.…”

Section: Introductionmentioning

confidence: 99%

Option implied ambiguity and its information content: Evidence from the subprime crisis

Driouchi

Trigeorgis

2015

Ann Oper Res

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This paper studies option investors' tendency to deviate from risk-neutrality around extreme financial events. We incorporate ambiguity into Black-Scholes theory and analyze the lead-lag association between option and stock markets during 2006-2008. Our findings from the Standard and Poor's 500 index options reveal that investors' option implied ambiguity moderates the lead-lag relationship between implied and realized volatility. We find that implied ambiguity contains predictive realized volatility information (beyond constant and stochastic implied volatilities), and that implied volatility is a less biased predictor of realized market variance when accounting for ambiguity in option pricing. We are also able to track changing investors' ambiguity perceptions (pessimism or optimism) prior to severe volatility events and document shifts in ambiguity aversion among put option holders in the period leading to the fall 2008 global market crash. Our results hold under multiple-priors and Choquet ambiguity specifications.

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“…There is a growing body of literature that applies the super-hedging approach to asset pricing with model uncertainty, for example, Epstein and Ji (2013), Mykland (2000) and Vorbrink (2014). Araujo et al (2002) show that the super-hedging pricing approach is natural to study the Arrow-Debreu valuation problem with ambiguity. In this section, we propose a general concept of true asset price under model uncertainty.…”

Section: Examplementioning

confidence: 99%

Model Uncertainty Effect on Asset Prices

Jiang

Tian

2017

Int Rev Finance

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We develop a weighted‐average approach of pricing under model uncertainty, where several plausible models are considered instead of a perfect one. The model uncertainty effect from this weighted‐average approach is significantly different from the conventional wisdom, in which the true price must be bounded by prices in all plausible models. We identify under what circumstances the model uncertainty effect is significant and reveal serious risk management challenges for researchers, regulators, and market participants.

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Pricing rules and Arrow–Debreu ambiguous valuation

Cited by 27 publications

References 43 publications

Equilibria Under Knightian Price Uncertainty

Equilibria Under Knightian Price Uncertainty

Option implied ambiguity and its information content: Evidence from the subprime crisis

Model Uncertainty Effect on Asset Prices

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