On securitization, market completion and equilibrium risk transfer

Horst, Ulrich; Pirvu, Traian A.; Reis, Gonçalo dos

doi:10.1007/s11579-010-0022-1

“…We refer to Horst and Müller (2007) and Horst et al (2010) for sufficient conditions for market completeness in continuous-time and characterization of equilibrium by BSDEs (backward stochastic differential equations). Results on market completeness in more general equilibrium models can be found in Magill and Shafer (1990) and Anderson and Raimondo (2009). …”

Section: First Order Conditions and Equilibrium Dynamicsmentioning

confidence: 99%

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Cheridito

¹

,

Horst

²

,

Kupper

³

et al. 2016

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We provide results on the existence and uniqueness of equilibrium in dynamically incomplete financial markets in discrete time. Our framework allows for heterogeneous agents, unspanned random endowments and convex trading constraints. In the special case where all agents have preferences of the same type and all random endowments are replicable by trading in the financial market we show that a one-fund theorem holds and give an explicit expression for the equilibrium pricing kernel. If the underlying noise is generated by finitely many Bernoulli random walks, the equilibrium dynamics can be described by a system of coupled backward stochastic difference equations, which in the continuous-time limit becomes a multi-dimensional backward stochastic differential equation. If the market is complete in equilibrium, the system of equations decouples, but if not, one needs to keep track of the prices and continuation values of all agents to solve it. As an example we simulate option prices in the presence of stochastic volatility, demand pressure and short-selling constraints.JEL classification: C62, D52, D53

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“…Cheridito et al [3] follow in the footsteps of Horst et al [11] to solve a problem of valuing a derivative in an incomplete market by equilibrium considerations. In Horst et al [11], the problem can be solved in a one-dimensional framework, since the derivative is assumed to complete the market.…”

Section: Lemma 32 There Is a One-to-one Correspondence Between The Fmentioning

confidence: 99%

“…In Horst et al [11], the problem can be solved in a one-dimensional framework, since the derivative is assumed to complete the market. Cheridito et al [3] do not impose this condition, which makes the analysis much more involved.…”

Section: Lemma 32 There Is a One-to-one Correspondence Between The Fmentioning

confidence: 99%

A financial market with interacting investors: does an equilibrium exist?

Frei

¹

,

Reis

²

2011

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While trading on a financial market, the agents we consider take the performance of their peers into account. By maximizing individual utility subject to investment constraints, the agents may ruin each other even unintentionally so that no equilibrium can exist. However, when the agents are willing to waive little expected utility, an approximated equilibrium can be established. The study of the associated backward stochastic differential equation (BSDE) reveals the mathematical reason for the absence of an equilibrium. Presenting an illustrative counterexample, we explain why such multidimensional quadratic BSDEs may not have solutions despite bounded terminal conditions and in contrast to the one-dimensional case.

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“…If the market turns out to be complete in equilibrium, both our systems of BS∆Es and BSDEs decouple. Conditions that guarantee market completeness in equilibrium have been studied in various frameworks; see for instance, Magill and Shafer (1990), Horst and Müller (2007), Anderson and Raimondo (2009) or Horst et al (2010). However, if the market is incomplete in equilibrium, our equations do not decouple, and to solve it one has to keep track of the prices and the continuation values of all agents.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Cheridito

¹

,

Horst

²

,

Kupper³

et al. 2011

Self Cite

View full text Add to dashboard Cite

We provide results on the existence and uniqueness of equilibrium in dynamically incomplete financial markets in discrete time. Our framework allows for heterogeneous agents, unspanned random endowments and convex trading constraints. In the special case where all agents have preferences of the same type and all random endowments are replicable by trading in the financial market we show that a one-fund theorem holds and give an explicit expression for the equilibrium pricing kernel. If the underlying noise is generated by finitely many Bernoulli random walks, the equilibrium dynamics can be described by a system of coupled backward stochastic difference equations, which in the continuous-time limit becomes a multi-dimensional backward stochastic differential equation. If the market is complete in equilibrium, the system of equations decouples, but if not, one needs to keep track of the prices and continuation values of all agents to solve it. As an example we simulate option prices in the presence of stochastic volatility, demand pressure and short-selling constraints.JEL classification: C62, D52, D53

show abstract

On securitization, market completion and equilibrium risk transfer

Cited by 32 publications

References 40 publications

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

A financial market with interacting investors: does an equilibrium exist?

Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences

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