A characterization of the distributions that imply existence of linear equilibria in the Kyle-model

Nöldeke, Georg; Tröger, Thomas

doi:10.1007/s10436-005-0024-9

Cited by 12 publications

(5 citation statements)

References 16 publications

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“…Finally, it should be pointed out that the combined assumptions of our model are crucial in characterizing Proposition 1 expressions. Indeed, many research papers which studied the existence and uniqueness of [11] type model, either considered the case of a single or multiple insider(s), with perfect observation of the stock value (see, [14] , [15] , [16] ). Moreover, our model, similar to [12] model, studied [11] in a complex environment with partially informed traders.…”

Section: The Modelmentioning

confidence: 99%

“…Recently, [5] extended [11] to the case of two insiders, one risk-neutral and one risk-averse, while [10] studied the case of two insiders in which the first insider is risk-neutral while the second insider is overconfident. Among other extensions, are a group of papers interested in proving the existence (or not) and/or uniqueness of Kyle-type model equilibria (See for example, [3] , [4] , [5] , [6] , [12] , [14] , [15] , [16] , [19] ). This paper belongs to the latter type of extensions, more specifically, it extended [11] to the general case of information correlation between the two insiders.…”

Section: Introductionmentioning

confidence: 99%

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Existence of linear equilibria in the Kyle model with partial correlation and two risk neutral traders

Daher

Saleeby²

2023

Heliyon

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Existence of linear equilibria in the Kyle model with partial correlation and two risk neutral traders

Daher

Saleeby²

2023

Heliyon

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“…So while the questions are related, our results and those of the above papers are not directly comparable. 5 See also Nöldeke andTröger (2001, 2006) for the analysis of the role of the normality assumption for the existence of linear equilibria in one-period models in the spirit of Kyle (1985), with multiple strategic traders who receive perfect signals about the value of the asset. with the correlations of signals being stronger for traders who are closer to each other (in this model, as in the Rostek and Weretka (2012) model discussed above, all traders use identical strategies in equilibrium).…”

Section: Related Literaturementioning

confidence: 99%

Strategic Trading in Informationally Complex Environments

Lambert¹,

Ostrovsky²,

Panov³

2018

Econometrica

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This supplement contains additional results and proofs omitted from the main paper. S.1. ZERO AGGREGATE DEMAND IN EQUILIBRIUMIN THIS SECTION, we formally derive equilibria in the special examples in which aggregate demand ends up being zero on the equilibrium path (footnote 12 in Section 2.2 and footnote 20 in Section 5). In Section S.1.1, we work out the example with one informed trader, corresponding to footnote 12, and in Section S.1.2, we work out the example with multiple informed traders, corresponding to footnote 20. S.1.1. One Informed Trader EXAMPLE S.1: The value of the security, v, is distributed normally with mean 0 and variance 1. There is one strategic trader with signal θ 1 who observes the value perfectly: θ 1 = v. The demand of liquidity traders is u = −v. The market maker does not observe any signals beyond the aggregate demand.This example satisfies Assumptions 1 and 2 in Section 3, and thus we can use the closedform solutions derived in the proof of Theorem 1 and presented in Section 3.2 of the paper (for the special case k M = 0). Because we have only one strategic trader in the example, many of the matrices become scalars, simplifying the calculation.Specifically, Σ θθ = Σ diag = 1, and, therefore, Λ = 2 and Λ −1 = 1/2. Next, Σ θv = 1, while This example also satisfies Assumptions 1 and 2 in Section 2, and thus we can use the closed-form solutions derived in the proof of Theorem 1 and presented in Section 3.2 (again, for the special case k M = 0). We now have multiple strategic traders, so the calculations involve matrix manipulations.Specifically, Σ θθ is an m-dimensional matrix whose elements are all equal to 1, while Σ diag is an m-dimensional identity matrix. We thus haveThe coefficients of the quadratic equation on γ are, therefore2 , and c = 1/(m + 1) 2 , which in turn gives us γ = 1/m and β D = m. Thus,and so on the equilibrium path, aggregate demand is equal toThus, for every m, the market price on the equilibrium path is also always equal to 0, not revealing any information contained in the signals of the strategic traders and in the demand coming from the liquidity traders. S.2. ZERO INTERCEPTS IN EQUILIBRIUMIn this section, we prove the statement made informally in footnote 13 in Section 3.2 that in our setting, linear equilibria with nonzero intercepts do not exist. PROPOSITION S.1: Suppose there exists an equilibrium of the formThen β 0 = 0 and for all i, δ i = 0.PROOF: Consider a particular realization of θ i , θ M , and u. Then in this equilibrium, the realized price will be given byBy the definition of equilibrium, for every realization of θ M and D, the price set by the market maker is equal to the expected value of the security conditional on θ M and D:Integrating over all possible realizations of θ M and D, we thus get, for the unconditional expectation of the price,Since by assumption, E[v] = 0, and also E[θ M ], E[u], and E[θ i ] (for all i) are equal to 0, by taking the unconditional expectation of Equation (S.1), we getNow, as inStep 2 of the proof of Theorem 1, consi...

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“…Tail distributions, however, of normal distributions are not normal. Thus, despite the theoretical desirability of the normal distribution that has been pointed out by Nöldeke and Tröger [25,26] and Bagnoli, Viswanathan, and Holden [4], it is preferable in our situation to consider a set-up with uniform distributions, just because the tail distribution of a uniform distribution is again uniform. We will assume therefore in the sequel that the random variables X 0 , Y , and V are uniformly distributed on intervals…”

Section: Trading In the Swap Marketmentioning

confidence: 99%

Manipulation in Money Markets

et al. 2006

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Interest rate derivatives are among the most actively traded financial instruments in the main currency areas. With values of positions reacting immediately to the underlying index of daily interbank rates, manipulation has become an increasing challenge for the operational implementation of monetary policy. To address this issue, we study a microstructure model in which a commercial bank may have strategic recourse to central bank standing facilities. We characterise an equilibrium in which market rates will be manipulated with strictly positive probability. Our findings have an immediate bearing on recent developments in the Sterling and Euro money markets. Interest rate derivatives are among the most actively traded financial instruments in the main currency areas. With values of positions reacting immediately to the underlying index of daily interbank rates, manipulation has become an increasing challenge for the operational implementation of monetary policy. To address this issue, we study a microstructure model in which a commercial bank may have strategic recourse to central bank standing facilities. We characterise an equilibrium in which market rates will be manipulated with strictly positive probability. Our findings have an immediate bearing on recent developments in the Sterling and Euro money markets. Manipulation in Money MarketsJEL classification: D84, E52

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A characterization of the distributions that imply existence of linear equilibria in the Kyle-model

Cited by 12 publications

References 16 publications

Existence of linear equilibria in the Kyle model with partial correlation and two risk neutral traders

Existence of linear equilibria in the Kyle model with partial correlation and two risk neutral traders

Strategic Trading in Informationally Complex Environments

Manipulation in Money Markets

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