Information and Default Risk in Financial Valuation
Abstract: This thesis consists of an introduction and five articles in the field of financial mathematics. The main topics of the papers comprise credit risk modelling, optimal stopping theory, and Dynkin games. An underlying theme in all of the articles is valuation of various financial instruments. Namely, Paper I deals with valuation of a game version of a perpetual American option where the parties disagree about the distributional properties of the underlying process, Papers II and III investigate pricing of default-sensitive contingent claims, Paper IV treats CVA (credit value adjustment) modelling for a portfolio consisting of American options, and Paper V studies a problem motivated by model calibration in pricing of corporate bonds.In each of the articles, we deal with an underlying stochastic process that is continuous in time and defined on some probability space. Namely, Papers I-IV treat stochastic processes with continuous paths, whereas Paper V assumes that the underlying process is a jump-diffusion with finite jump intensity.The information level in Paper I is the filtration generated by the stock value. In articles III and IV, we consider investors whose information flow is designed as a progressive enlargement with default time of the filtration generated by the stock price, whereas in Paper II the information flow is an initial enlargement. Paper V assumes that the default is a hitting time of the firm's value and thus the underlying filtration is the one generated by the process modelling this value.Moreover, in all of the papers the risk-free bonds are assumed for simplicity to have deterministic prices so that the focus is on the uncertainty coming from the stock price and default risk.
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