Quantitative Methods for the Study of Firm Capital Values

The research will be focused on the dynamics of the capital value of firms with capital structure composed uniquely by assets actively traded in financial markets. In this research proposal, I will refer to the market value of the outstanding securities of a firm as its capital value. The research will be composed of three parts. The first part of the research will be devoted to the development of an appropriate structural model for the formation of the capital value for a firm with specific financial characteristics (e.g. carrying out activities in the same sector and country and having the same credit rating). This model will account for several risk factors whose dynamics will be nonparametric and it will be consistent with the no-arbitrage hypotheses in the markets of the securities issued by the firm. The second part of the research will be dedicated to the development of an estimation methodology for the model. Finally, the third part of the research will be devoted to empirical studies of the firm's probability of default and the firm's regulatory capital, which is the capital that the firm is required to allocate by regulators in a given class of assets. The novelty of the research will stem from the approach and the potential results. I will employ the methodologies for the study of bond prices developed in the project 'Pricing Bonds with American-Style Features Accounting for Model Risk' to extract information on the process that generates the value of the firm's outstanding debt.Idiosyncratic factors are the sources of the risks faced by a particular firm. Systematic factors give rise to the risks that a firm shares with other companies. Considering idiosyncratic risks, in relation to peculiar characteristics of a firm is important to describe the dynamics of the firm's capital value at the micro-economic level. Considering systematic risks in relation to some macroeconomic and financial market conditions is fundamental to study the factors affecting the capital value of different firms. The structural model will account for both idiosyncratic and systematic factors for a firm's capital value.Since there is not a consensus between experts on the determinants of a firm's capital value, the model will accommodate both observable and unobservable common factors. Considering unobservable factors will lower the risk of omission of important factors. The model setting will be in discrete time, so that there will be no need to consider issues related to the time discretization. The model, which will be different from the ones used in the existing literature on quantitative studies of the firm's capital structure, will be estimated by means of the techniques developed in the project 'Pricing Bonds with American-Style Features Accounting for Model Risk' and some modern econometric techniques for panel data with latent factors.Some applications of the proposed methodology will be provided. Priority will be given to the study of the firm's probability of default and to applications that are useful from the perspective of a financial regulator. I will consider detection tools for events that could threaten the financial stability of some firms and I will study micro- and macro-prudential tools. Among the detection tools, I will consider some devices to follow higher uncertainty regarding a firm's capital value. Among the prevention tools, I will analyze the firm's regulatory capital and Contingent Convertible bonds (CoCos).