Zachary Feinstein | Stevens Institute of Technology (original) (raw)

Papers by Zachary Feinstein

In this paper we will consider a generalized extension of the Eisenberg-Noe model of financial co... more In this paper we will consider a generalized extension of the Eisenberg-Noe model of financial contagion to allow for time dynamics in both discrete and continuous time. Derivation and interpretation of the financial implications will be provided. Emphasis will be placed on the continuous-time framework and its formulation as a differential equation driven by the operating cash flows. Mathematical results on existence and uniqueness of firm wealths under the discrete and continuous-time models will be provided. Finally, the financial implications of time dynamics will be considered. The focus will be on how the dynamic clearing solutions differ from those of the static Eisenberg-Noe model.

In this paper we present formulas for the valuation of debt and equity of firms in a financial ne... more In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with consistent marginal endowments. Such financial networks encode the interconnection of firms through debt claims. The proposed pricing formulas consider the realized, endogenous, recovery rate on debt claims. Special consideration is given to the CAPM setting in which firms invest in correlated portfolios. We provide theoretical and empirical justifications for comonotonic endowments in the financial sector.

We consider a network of banks that optimally choose a strategy of asset liquidations and borrowi... more We consider a network of banks that optimally choose a strategy of asset liquidations and borrowing in order to cover short term obligations. The borrowing is done in the form of collateralized repurchase agreements, the haircut level of which depends on the total liquidations of all the banks. Similarly the fire-sale price of the asset obtained by each of the banks depends on the amount of assets liquidated by the bank itself and by other banks. By nature of this setup, banks' behavior is considered as a Nash equilibrium. This paper provides two forms for market clearing to occur: through a common closing price and through an application of the limit order book. The main results of this work are providing sufficient conditions for existence and uniqueness of the clearing solutions (i.e., liquidations, borrowing, fire sale prices, and haircut levels).

In this paper we present results on scalar risk measures in markets with transaction costs. Such ... more In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We w...

In this paper, we study the financial and economic implications of a zombie epidemic on a major i... more In this paper, we study the financial and economic implications of a zombie epidemic on a major industrialized nation. We begin with a consideration of the epidemiological modeling of the zombie contagion. The emphasis of this work is on the computation of direct and indirect financial consequences of this contagion of the walking dead. A moderate zombie outbreak leaving 1 million people dead in a major industrialized nation could result in GDP losses of 23.44% over the subsequent year and a drop in financial market of 29.30%. We conclude by recommending policy actions necessary to prevent this potential economic collapse.

arXiv: General Finance, 2015

In this paper we study the financial repercussions of the destruction of two fully armed and oper... more In this paper we study the financial repercussions of the destruction of two fully armed and operational moon-sized battle stations ("Death Stars") in a 4-year period and the dissolution of the galactic government in Star Wars. The emphasis of this work is to calibrate and simulate a model of the banking and financial systems within the galaxy. Along these lines, we measure the level of systemic risk that may have been generated by the death of Emperor Palpatine and the destruction of the second Death Star. We conclude by finding the economic resources the Rebel Alliance would need to have in reserve in order to prevent a financial crisis from gripping the galaxy through an optimally allocated banking bailout.

We introduce a heterogeneous version of a contagious McKean–Vlasov system whose heterogeneity has... more We introduce a heterogeneous version of a contagious McKean–Vlasov system whose heterogeneity has a natural and particularly tractable structure. It is shown that this system characterises the limit points of a finite particle system with applications to solvency contagion in interbank markets and coupled integrate-and-fire models in mathematical neuroscience. Furthermore, we provide a result on global uniqueness for the full common noise system under a simple smallness condition on the strength of interactions, and we show that there is a unique differentiable solution up to an explosion time in the system without common noise.

arXiv: General Finance, 2017

Gringotts Wizarding Bank is well known as the only financial institution in all of the Wizarding ... more Gringotts Wizarding Bank is well known as the only financial institution in all of the Wizarding UK as documented in the works recounting the heroics of Harry Potter. The concentration of power and wealth in this single bank needs to be weighed against the financial stability of the entire Wizarding economy. This study will consider the impact to financial risk of breaking up Gringotts Wizarding Bank into five component pieces, along the lines of the Glass-Steagall Act in the United States. The emphasis of this work is to calibrate and simulate a model of the banking and financial systems within Wizarding UK under varying stress test scenarios simulating rumors of Lord Voldemort's return or the release of magical creatures into an unsuspecting muggle populace. We conclude by comparing the economic fallout from financial crises under the two systems: (i) Gringotts Wizarding Bank as a monopoly and (ii) the split-up financial system. We do this comparison on the level of minimal sy...

In this work we introduce a model of default contagion that combines the approaches of Eisenberg-... more In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in a network of financial institutions. The main result is to demonstrate a mean field interaction that can be found as the limit of the finite bank system generated from a finite Eisenberg-Noe style network. In this way, we connect two previously disparate frameworks for systemic risk, and in turn we provide a bridge for exploiting recent advances in mean field analysis when modelling systemic risk. The mean field limit is shown to be well-posed and is identified as a certain conditional McKean-Vlasov type problem that respects the original network topology under suitable assumptions.

In this paper, we propose a clearing model for prices in a financial markets due to margin calls ... more In this paper, we propose a clearing model for prices in a financial markets due to margin calls on short sold assets. In doing so, we construct an explicit formulation for the prices that would result immediately following asset purchases and a margin call. The key result of this work is the determination of a threshold short interest ratio which, if exceeded, results in the discontinuity of the clearing prices due to a feedback loop. This model and threshold short interest ratio is then compared with data from early 2021 to consider the observed price movements of GameStop, AMC, and Naked Brand which have been targeted for a short squeeze by retail investors and, prominently, by the online community r/WallStreetBets.

arXiv: Mathematical Finance, 2018

In this paper we present formulas for the valuation of debt and equity of firms in a financial ne... more In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with consistent marginal endowments. Such financial networks encode the interconnection of firms through debt claims. The proposed pricing formulas consider the realized, endogenous, recovery rate on debt claims. Special consideration is given to the CAPM setting in which firms invest in correlated portfolios; in the comonotonic framework this corresponds to the setting in which firms only invest in a risk-free bond and a common risky asset following a geometric Brownian motion.

arXiv: Mathematical Finance, 2020

In this work we provide a simple setting that connects the structural modelling approach of Gai-K... more In this work we provide a simple setting that connects the structural modelling approach of Gai-Kapadia interbank networks with the mean-field approach to default contagion. To accomplish this we make two key contributions. First, we propose a dynamic default contagion model with endogenous early defaults for a finite set of banks, generalising the Gai-Kapadia framework. Second, we reformulate this system as a stochastic particle system leading to a limiting mean-field problem. We study the existence of these clearing systems and, for the mean-field problem, the continuity of the system response.

arXiv: Mathematical Finance, 2019

In this work we introduce a model of default contagion that combines the approaches of Eisenberg-... more In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in a network of financial institutions. The main result is to demonstrate a mean field interaction that can be found as the limit of the finite bank system generated from a finite Eisenberg-Noe style network. In this way, we connect two previously disparate frameworks for systemic risk, and in turn we provide a bridge for exploiting recent advances in mean field analysis when modelling systemic risk. The mean field limit is shown to be well-posed and is identified as a certain conditional McKean-Vlasov type problem that respects the original network topology under suitable assumptions.

Capital Markets: Market Microstructure eJournal, 2020

In this work we present an equilibrium formulation for price impacts. This is motivated by the Bu... more In this work we present an equilibrium formulation for price impacts. This is motivated by the Buhlmann equilibrium in which assets are sold into a system of market participants and can be viewed as a generalization of the Esscher premium. Existence and uniqueness of clearing prices for the liquidation of a portfolio are studied. We also investigate other desired portfolio properties including monotonicity and concavity. Price per portfolio unit sold is also calculated. In special cases, we study price impacts generated by market participants who follow the exponential utility and power utility.

arXiv: General Finance, 2020

In this paper, we study the financial and economic implications of a zombie epidemic on a major i... more In this paper, we study the financial and economic implications of a zombie epidemic on a major industrialized nation. We begin with a consideration of the epidemiological modeling of the zombie contagion. The emphasis of this work is on the computation of direct and indirect financial consequences of this contagion of the walking dead. A moderate zombie outbreak leaving 1 million people dead in a major industrialized nation could result in GDP losses of 23.44% over the subsequent year and a drop in financial market of 29.30%. We conclude by recommending policy actions necessary to prevent this potential economic collapse.

arXiv: Risk Management, 2013

This paper contains an overview of results for dynamic risk measures in markets with transaction ... more This paper contains an overview of results for dynamic risk measures in markets with transaction costs. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approaches compare to each other.

Research Papers in Economics, 2020

Mobiliser des liquidites lorsqu’il y a des difficultes de financement exerce des pressions sur le... more Mobiliser des liquidites lorsqu’il y a des difficultes de financement exerce des pressions sur le marche financier. Liquider de grandes quantites d’actifs fait baisser leur prix et peut amplifier les chocs de financement. Comment les mesures prises par les banques pour surmonter une crise de financement accroissent-elles le risque de contagion? Nous proposons un modele permettant d’etudier la transmission des difficultes au sein d’un systeme bancaire ebranle par un choc de financement. Le modele prend en compte 1) les effets indirects qui decoulent de l’incidence sur les prix d’un reinvestissement optimal de l’actif des banques et 2) les effets de reseau observes si les banques ne sont pas en mesure de rembourser tout ce qu’elles doivent aux autres banques (expositions interbancaires directes). Nous demontrons comment, et a quel prix, les banques liquident leurs actifs a l’equilibre, et examinons le role des organismes de reglementation sur la stabilisation des prix pendant une cr...

In this paper we will consider a generalized extension of the Eisenberg-Noe model of financial co... more In this paper we will consider a generalized extension of the Eisenberg-Noe model of financial contagion to allow for time dynamics in both discrete and continuous time. Derivation and interpretation of the financial implications will be provided. Emphasis will be placed on the continuous-time framework and its formulation as a differential equation driven by the operating cash flows. Mathematical results on existence and uniqueness of firm wealths under the discrete and continuous-time models will be provided. Finally, the financial implications of time dynamics will be considered. The focus will be on how the dynamic clearing solutions differ from those of the static Eisenberg-Noe model.

In this paper we present formulas for the valuation of debt and equity of firms in a financial ne... more In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with consistent marginal endowments. Such financial networks encode the interconnection of firms through debt claims. The proposed pricing formulas consider the realized, endogenous, recovery rate on debt claims. Special consideration is given to the CAPM setting in which firms invest in correlated portfolios. We provide theoretical and empirical justifications for comonotonic endowments in the financial sector.

We consider a network of banks that optimally choose a strategy of asset liquidations and borrowi... more We consider a network of banks that optimally choose a strategy of asset liquidations and borrowing in order to cover short term obligations. The borrowing is done in the form of collateralized repurchase agreements, the haircut level of which depends on the total liquidations of all the banks. Similarly the fire-sale price of the asset obtained by each of the banks depends on the amount of assets liquidated by the bank itself and by other banks. By nature of this setup, banks' behavior is considered as a Nash equilibrium. This paper provides two forms for market clearing to occur: through a common closing price and through an application of the limit order book. The main results of this work are providing sufficient conditions for existence and uniqueness of the clearing solutions (i.e., liquidations, borrowing, fire sale prices, and haircut levels).

In this paper we present results on scalar risk measures in markets with transaction costs. Such ... more In this paper we present results on scalar risk measures in markets with transaction costs. Such risk measures are defined as the minimal capital requirements in the cash asset. First, some results are provided on the dual representation of such risk measures, with particular emphasis given on the space of dual variables as (equivalent) martingale measures and prices consistent with the market model. Then, these dual representations are used to obtain the main results of this paper on time consistency for scalar risk measures in markets with frictions. It is well known from the superhedging risk measure in markets with transaction costs, as in Jouini and Kallal (1995), Roux and Zastawniak (2016), and Loehne and Rudloff (2014), that the usual scalar concept of time consistency is too strong and not satisfied. We will show that a weaker notion of time consistency can be defined, which corresponds to the usual scalar time consistency but under any fixed consistent pricing process. We w...

In this paper, we study the financial and economic implications of a zombie epidemic on a major i... more In this paper, we study the financial and economic implications of a zombie epidemic on a major industrialized nation. We begin with a consideration of the epidemiological modeling of the zombie contagion. The emphasis of this work is on the computation of direct and indirect financial consequences of this contagion of the walking dead. A moderate zombie outbreak leaving 1 million people dead in a major industrialized nation could result in GDP losses of 23.44% over the subsequent year and a drop in financial market of 29.30%. We conclude by recommending policy actions necessary to prevent this potential economic collapse.

arXiv: General Finance, 2015

In this paper we study the financial repercussions of the destruction of two fully armed and oper... more In this paper we study the financial repercussions of the destruction of two fully armed and operational moon-sized battle stations ("Death Stars") in a 4-year period and the dissolution of the galactic government in Star Wars. The emphasis of this work is to calibrate and simulate a model of the banking and financial systems within the galaxy. Along these lines, we measure the level of systemic risk that may have been generated by the death of Emperor Palpatine and the destruction of the second Death Star. We conclude by finding the economic resources the Rebel Alliance would need to have in reserve in order to prevent a financial crisis from gripping the galaxy through an optimally allocated banking bailout.

We introduce a heterogeneous version of a contagious McKean–Vlasov system whose heterogeneity has... more We introduce a heterogeneous version of a contagious McKean–Vlasov system whose heterogeneity has a natural and particularly tractable structure. It is shown that this system characterises the limit points of a finite particle system with applications to solvency contagion in interbank markets and coupled integrate-and-fire models in mathematical neuroscience. Furthermore, we provide a result on global uniqueness for the full common noise system under a simple smallness condition on the strength of interactions, and we show that there is a unique differentiable solution up to an explosion time in the system without common noise.

arXiv: General Finance, 2017

Gringotts Wizarding Bank is well known as the only financial institution in all of the Wizarding ... more Gringotts Wizarding Bank is well known as the only financial institution in all of the Wizarding UK as documented in the works recounting the heroics of Harry Potter. The concentration of power and wealth in this single bank needs to be weighed against the financial stability of the entire Wizarding economy. This study will consider the impact to financial risk of breaking up Gringotts Wizarding Bank into five component pieces, along the lines of the Glass-Steagall Act in the United States. The emphasis of this work is to calibrate and simulate a model of the banking and financial systems within Wizarding UK under varying stress test scenarios simulating rumors of Lord Voldemort's return or the release of magical creatures into an unsuspecting muggle populace. We conclude by comparing the economic fallout from financial crises under the two systems: (i) Gringotts Wizarding Bank as a monopoly and (ii) the split-up financial system. We do this comparison on the level of minimal sy...

In this work we introduce a model of default contagion that combines the approaches of Eisenberg-... more In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in a network of financial institutions. The main result is to demonstrate a mean field interaction that can be found as the limit of the finite bank system generated from a finite Eisenberg-Noe style network. In this way, we connect two previously disparate frameworks for systemic risk, and in turn we provide a bridge for exploiting recent advances in mean field analysis when modelling systemic risk. The mean field limit is shown to be well-posed and is identified as a certain conditional McKean-Vlasov type problem that respects the original network topology under suitable assumptions.

In this paper, we propose a clearing model for prices in a financial markets due to margin calls ... more In this paper, we propose a clearing model for prices in a financial markets due to margin calls on short sold assets. In doing so, we construct an explicit formulation for the prices that would result immediately following asset purchases and a margin call. The key result of this work is the determination of a threshold short interest ratio which, if exceeded, results in the discontinuity of the clearing prices due to a feedback loop. This model and threshold short interest ratio is then compared with data from early 2021 to consider the observed price movements of GameStop, AMC, and Naked Brand which have been targeted for a short squeeze by retail investors and, prominently, by the online community r/WallStreetBets.

arXiv: Mathematical Finance, 2018

In this paper we present formulas for the valuation of debt and equity of firms in a financial ne... more In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with consistent marginal endowments. Such financial networks encode the interconnection of firms through debt claims. The proposed pricing formulas consider the realized, endogenous, recovery rate on debt claims. Special consideration is given to the CAPM setting in which firms invest in correlated portfolios; in the comonotonic framework this corresponds to the setting in which firms only invest in a risk-free bond and a common risky asset following a geometric Brownian motion.

arXiv: Mathematical Finance, 2020

In this work we provide a simple setting that connects the structural modelling approach of Gai-K... more In this work we provide a simple setting that connects the structural modelling approach of Gai-Kapadia interbank networks with the mean-field approach to default contagion. To accomplish this we make two key contributions. First, we propose a dynamic default contagion model with endogenous early defaults for a finite set of banks, generalising the Gai-Kapadia framework. Second, we reformulate this system as a stochastic particle system leading to a limiting mean-field problem. We study the existence of these clearing systems and, for the mean-field problem, the continuity of the system response.

arXiv: Mathematical Finance, 2019

In this work we introduce a model of default contagion that combines the approaches of Eisenberg-... more In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in a network of financial institutions. The main result is to demonstrate a mean field interaction that can be found as the limit of the finite bank system generated from a finite Eisenberg-Noe style network. In this way, we connect two previously disparate frameworks for systemic risk, and in turn we provide a bridge for exploiting recent advances in mean field analysis when modelling systemic risk. The mean field limit is shown to be well-posed and is identified as a certain conditional McKean-Vlasov type problem that respects the original network topology under suitable assumptions.

Capital Markets: Market Microstructure eJournal, 2020

In this work we present an equilibrium formulation for price impacts. This is motivated by the Bu... more In this work we present an equilibrium formulation for price impacts. This is motivated by the Buhlmann equilibrium in which assets are sold into a system of market participants and can be viewed as a generalization of the Esscher premium. Existence and uniqueness of clearing prices for the liquidation of a portfolio are studied. We also investigate other desired portfolio properties including monotonicity and concavity. Price per portfolio unit sold is also calculated. In special cases, we study price impacts generated by market participants who follow the exponential utility and power utility.

arXiv: General Finance, 2020

In this paper, we study the financial and economic implications of a zombie epidemic on a major i... more In this paper, we study the financial and economic implications of a zombie epidemic on a major industrialized nation. We begin with a consideration of the epidemiological modeling of the zombie contagion. The emphasis of this work is on the computation of direct and indirect financial consequences of this contagion of the walking dead. A moderate zombie outbreak leaving 1 million people dead in a major industrialized nation could result in GDP losses of 23.44% over the subsequent year and a drop in financial market of 29.30%. We conclude by recommending policy actions necessary to prevent this potential economic collapse.

arXiv: Risk Management, 2013

This paper contains an overview of results for dynamic risk measures in markets with transaction ... more This paper contains an overview of results for dynamic risk measures in markets with transaction costs. We provide the main results of four different approaches. We will prove under which assumptions results within these approaches coincide, and how properties like primal and dual representation and time consistency in the different approaches compare to each other.

Research Papers in Economics, 2020

Mobiliser des liquidites lorsqu’il y a des difficultes de financement exerce des pressions sur le... more Mobiliser des liquidites lorsqu’il y a des difficultes de financement exerce des pressions sur le marche financier. Liquider de grandes quantites d’actifs fait baisser leur prix et peut amplifier les chocs de financement. Comment les mesures prises par les banques pour surmonter une crise de financement accroissent-elles le risque de contagion? Nous proposons un modele permettant d’etudier la transmission des difficultes au sein d’un systeme bancaire ebranle par un choc de financement. Le modele prend en compte 1) les effets indirects qui decoulent de l’incidence sur les prix d’un reinvestissement optimal de l’actif des banques et 2) les effets de reseau observes si les banques ne sont pas en mesure de rembourser tout ce qu’elles doivent aux autres banques (expositions interbancaires directes). Nous demontrons comment, et a quel prix, les banques liquident leurs actifs a l’equilibre, et examinons le role des organismes de reglementation sur la stabilisation des prix pendant une cr...