Kyle equilibrium under random price pressure

Corcuera, José Manuel; Nunno, Giulia Di; Fajardo, José

doi:10.1007/s10203-019-00231-4

Cited by 7 publications

(14 citation statements)

References 40 publications

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“…The above setup uses the standard definition of equilibrium as in Back [1]. The difference lies in the generalisation of the set of admissible pricing rules that in particular includes the ones used in the current literature (see, e.g., [2], [11], [12], [6], [9], [14], [13], and [19]). Moreover, the signal of the insider is not assumed to be Markovian, i.e.…”

Section: Model Setupmentioning

confidence: 99%

“…We will show that the pricing rule employed therein allows infinite profit for the insider that uses trading strategies with martingale component and describe the correct penalization of the martingale component that prevents such opportunities and ensures that the absolutely continuous strategies are optimal. 13 Although this model does not directly fit to the above framework at a first sight, the exponential character of τ allows us to view the setting of Back and Baruch (and a more general version studied in C ¸etin [9]) as an infinite horizon version of the Kyle model.…”

Section: Penalization In Actionmentioning

confidence: 99%

“…Back's result was the original justification for restricting the set of admissible controls of the insider to absolutely continuous ones and this restriction is now standard in the asymmetric information literature (see, e.g., [2], [11], [12], [6], [9], [14], [13], and [19]). In this paper we show that if we extend the class of pricing rules beyond harmonic functions of total order to include ones used in the recent literature, e.g.…”

Section: Introductionmentioning

confidence: 99%

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On Pricing Rules and Optimal Strategies in General Kyle--Back Models

Çetın¹,

Danilova²

2021

SIAM J. Control Optim.

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The folk result in Kyle-Back models states that the value function of the insider remains unchanged when her admissible strategies are restricted to absolutely continuous ones. In this paper we show that, for a large class of pricing rules used in current literature, the value function of the insider can be finite when her strategies are restricted to be absolutely continuous and infinite when this restriction is not imposed. This implies that the folk result doesn't hold for those pricing rules and that they are not consistent with equilibrium. We derive the necessary conditions for a pricing rule to be consistent with equilibrium and prove that, when a pricing rule satisfies these necessary conditions, the insider's optimal strategy is absolutely continuous, thus obtaining the classical result in a more general setting.This, furthermore, allows us to justify the standard assumption of absolute continuity of insider's strategies since one can construct a pricing rule satisfying the necessary conditions derived in the paper that yield the same price process as the pricing rules employed in the modern literature when insider's strategies are absolutely continuous.

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Section: Model Setupmentioning

confidence: 99%

Section: Penalization In Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Pricing Rules and Optimal Strategies in General Kyle--Back Models

Çetın¹,

Danilova²

2021

SIAM J. Control Optim.

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“…The above setup uses the standard definition of equilibirum as in Back [1]. The difference lies in the generalisation of the set of admissible pricing rules that in particular includes the ones used in the current literature (see, e.g., [2], [10], [11], [5], [8], [13], [12], and [18]). Moreover, the signal of the insider is not assumed to be Markovian contrary to the common assumption.…”

Section: Model Setupmentioning

confidence: 99%

“…Back's result was the original justification for restricting the set of admissible controls of the insider to absolutely continuous ones and this restriction is now standard in the asymmetric information literature (see, e.g., [2], [10], [11], [5], [8], [13], [12], and [18]). In this paper we show that if we extend the class of pricing rules beyond harmonic functions of total order to include ones used in the recent literature, e.g.…”

Section: Introductionmentioning

confidence: 99%

On pricing rules and optimal strategies in general Kyle-Back models

Çetın¹,

Danilova²

2018

Preprint

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Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

Yang

Huang

2020

Appl Math Optim

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In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise. constant since new private information is introduced every period caused by the deterministic changes in the noise trading volatility. Stochastic variation was also introduced in the noise trading volume by Foster and Viswanathan [15], and this model was then empirically tested to show the joint behavior of the price volatility, volume, and price impact. However, a noticeable shortcoming of these extensions is the assumption that the information is short-lived, which is not realistic. Later on, deterministic noise trading volatility was directly incorporated into the Kyle model so that intra-day patterns of liquidity trading can be successfully captured [4]. Such an assumption on the noise trading volatility is still not appropriate since it gives rise to the deterministic price impact and further leads to the situation where expected execution costs of liquidity traders do not depend on the timing of their trading. A more recent extension to the Kyle model was proposed by Collin-Dufresne and Fos [11], who considered stochastic noise trading volatility, and showed that this is the only guarantee that insider's liquidity timing option can generate a stochastic price volatility as well as a nonzero correlation among the price volatility, market depth, and uninformed trading volume.Despite all the advantages of the model proposed in [11], it has not taken into consideration that the volatility is characterized by long memory, which is a consensus among financial econometricians. In particular, Bollerslev and Jubinski [7] presented the evidence of long memory in the volatility and investigated the extent to which the volume and volatility share common long-run dependencies. In line with this, they also proposed that the mixture-of-distributions hypotheses (MDH) might be better viewed as long-run proposition, after observing that occasional structural breaks can give rise to long-range dependence [17]. This implies long-range dependence could be induced under the MDH by occasional changes in the mean and/or volatility of the intra-day volumes and returns, which are generated due to the reaction traders make to information events. Furthermore, fractionally-integrated models were shown to provide a useful description of volatility dynamics in the presence of structural breaks because they effectively allow the unconditional ...

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Kyle equilibrium under random price pressure

Cited by 7 publications

References 40 publications

On Pricing Rules and Optimal Strategies in General Kyle--Back Models

On Pricing Rules and Optimal Strategies in General Kyle--Back Models

On pricing rules and optimal strategies in general Kyle-Back models

Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

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