A balance sheet model and its applications in budgeting simulations and credit risk

In this thesis we create a new mathematical accounting model that will give us not only a better comprehension of the firm and its dynamics, but also the possibility to fit in with financial and economic models already presented in economic literature, for example structural credit risk models. In order to develop a similar framework in the first chapter we review both the accounting literature involved with our purposes and a part of the financial literature concerns with credit risk models. In the second chapter starting from the balance sheet, known to be the most important source of information for a company, both at the internal and external level, we show an initial quantitative model which uses accounting data to represent the dynamics of the company and to create a simulation associated with those dynamics. Specifically, this application is based on the idea of representing the dynamics of a balance sheet via a series of difference equations, with the a priori assumption that accounting procedures can be mathematically axiomatized. In the third chapter we consider a version of the dynamic budgeting model previously introduced where parameters are constant. We investigate the implications of the constant parameters assumption on the liquidity process, which in our framework has a precise meaning and can be expressed in closed form. What is more, using the notion of average in the sense of Chisini and exploiting the properties of the double entry bookkeeping, we find the set of constant parameters that matches the results of the general model at each financial statement. A series of numerical exercises together with a sensitivity analysis illustrate the potentiality of our approach. In the last chapter we introduce a new structural model. It seems to be the first model linking the Credit Risk literature with the Financial Statement analysis in the sense that we deduce the default boundary levels based on book value quantities. It will be accomplished by extending the original Merton approach for credit risk to the presence of a cash shortage constraint. Mathematically speaking, we introduce in the call payoff defining the value of the Equity the presence of the liquidity shortage, in such a way that the payoff becomes a basket option on partially correlated assets, namely the asset value of the firm, the (stochastic) liquidity process and the (stochastic) debt process. Our approach is flexible enough to allow the computation of the relevant credit features like default probability and related benchmarks. This new approach is in line with the empirical results (see e.g. Davydenko 2005 and 2010).