In this thesis we intend to introduce a new theoretical framework that will allow us to define a new set of balance sheet mathematical models. In the first chapter after a historical introduction about the long and close relationship between mathematics and accounting we will focus on the in depth mathematical analysis, present in literature, of the double-entry book-keeping tool. To this day the double entry bookkeeping system can be considered as the reference mathematical theoretical framework of the accounting practice and thinking. The result of this analysis, combined with the results already present in literature about the dynamic representation of the balance sheet through first order finite difference linear systems, will enable us to introduce a new idea relating to a vector specifically built to describe the link between a single accounting item and the liquidity. We called it brick-vector since we can build a balance sheet model merging into an algebraic system the brick-vectors of all the accounting items chosen for our modelization. In order to start applying this class of models we close the first chapter presenting an averaging procedure (based on the concept of functional mean according to Chisini) that allows us to reduce the impact of the inevitably high number of variables that a balance sheet model time series brings with itself. In the second chapter we intend to show some of the possibilities offered by the brick vector formalization applying it to the problem of the cash flow risk assessment. Firstly we present a medium firm balance sheet model and we explore its closed form solution. Then we perform on the model our Chisini averaging procedure during which we present its relative mathematical shape. Finally after the introduction of a sensitivity analysis, in order to show some of the descriptive capabilities of the model, we apply it to the problem of cash flow risk assessment. We present the approaches proposed so far toward the issue of the computation of CFaR (Cash Flow at Risk) and then we propose our new methodology. It has the goal to overcome some of the main shortcomings of the previous approaches through the creation of a link between the accounting data, summarizing the firm’s business structure, and some macroeconomic drivers of particular importance. We end the chapter presenting a case study relating to Alitalia airlines where we apply the model to its balance sheet data and we perform our CFaR evaluation. In the third chapter we intend to keep on exploring the potential of the brick vector formalization applying it to the problem of the liquidity risk assessment in the banking sector. After an introduction to the issue of liquidity risk as well as that of the bank’s balance sheet modeling we present a commercial bank balance sheet model. Then we show its closed form solution and we perform our averaging procedure. We display the commercial bank balance sheet model evolution through a simulation aiming to portray the behavior of medium sized Italian commercial bank. Finally we discuss the problem of the liquidity risk assessment and we propose a new liquidity risk measure, tailored on the issue of funding liquidity, which is based on the CFaR methodology presented in the previous chapter. We called this new measure FLaR (Funding Liquidity at Risk) and through its medium-term time perspective it is meant to complement the role performed by the LaR (Liquidity at Risk) instrument in a short-term temporal perspective. We close the chapter presenting some future possible developments in the application of the brick vector framework to the liquidity risk assessment issue. Finally we conclude our thesis reviewing its content in relation to its goal to try to bridge the gap between the accounting field and other research areas of the economic science as well as the world of economic theory with that of economic practice.

A New Mathematical Framework for the Balance Sheet Dynamic Modeling applied to CFaR and LaR

GENTILI, Luca
2017-01-01

Abstract

In this thesis we intend to introduce a new theoretical framework that will allow us to define a new set of balance sheet mathematical models. In the first chapter after a historical introduction about the long and close relationship between mathematics and accounting we will focus on the in depth mathematical analysis, present in literature, of the double-entry book-keeping tool. To this day the double entry bookkeeping system can be considered as the reference mathematical theoretical framework of the accounting practice and thinking. The result of this analysis, combined with the results already present in literature about the dynamic representation of the balance sheet through first order finite difference linear systems, will enable us to introduce a new idea relating to a vector specifically built to describe the link between a single accounting item and the liquidity. We called it brick-vector since we can build a balance sheet model merging into an algebraic system the brick-vectors of all the accounting items chosen for our modelization. In order to start applying this class of models we close the first chapter presenting an averaging procedure (based on the concept of functional mean according to Chisini) that allows us to reduce the impact of the inevitably high number of variables that a balance sheet model time series brings with itself. In the second chapter we intend to show some of the possibilities offered by the brick vector formalization applying it to the problem of the cash flow risk assessment. Firstly we present a medium firm balance sheet model and we explore its closed form solution. Then we perform on the model our Chisini averaging procedure during which we present its relative mathematical shape. Finally after the introduction of a sensitivity analysis, in order to show some of the descriptive capabilities of the model, we apply it to the problem of cash flow risk assessment. We present the approaches proposed so far toward the issue of the computation of CFaR (Cash Flow at Risk) and then we propose our new methodology. It has the goal to overcome some of the main shortcomings of the previous approaches through the creation of a link between the accounting data, summarizing the firm’s business structure, and some macroeconomic drivers of particular importance. We end the chapter presenting a case study relating to Alitalia airlines where we apply the model to its balance sheet data and we perform our CFaR evaluation. In the third chapter we intend to keep on exploring the potential of the brick vector formalization applying it to the problem of the liquidity risk assessment in the banking sector. After an introduction to the issue of liquidity risk as well as that of the bank’s balance sheet modeling we present a commercial bank balance sheet model. Then we show its closed form solution and we perform our averaging procedure. We display the commercial bank balance sheet model evolution through a simulation aiming to portray the behavior of medium sized Italian commercial bank. Finally we discuss the problem of the liquidity risk assessment and we propose a new liquidity risk measure, tailored on the issue of funding liquidity, which is based on the CFaR methodology presented in the previous chapter. We called this new measure FLaR (Funding Liquidity at Risk) and through its medium-term time perspective it is meant to complement the role performed by the LaR (Liquidity at Risk) instrument in a short-term temporal perspective. We close the chapter presenting some future possible developments in the application of the brick vector framework to the liquidity risk assessment issue. Finally we conclude our thesis reviewing its content in relation to its goal to try to bridge the gap between the accounting field and other research areas of the economic science as well as the world of economic theory with that of economic practice.
2017
Balance sheet, Mathematical model, Difference equation system, Closed form solution, Dynamical balance sheet model, Cash Flow, Liquidity, risk, CFaR, LaR
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Descrizione: Doctoral thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/959681
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