Dynamic learning effect in corporate finance and risk management

One of the traditional ways to model uncertainty in finance is through some diffusion process assuming that parameters of this process were known. However this assumption is hardly realistic. Indeed, while many financial variables are certainly observable, it is impossible to claim that parameters of the processes that describe the evolution of those variables, such as drift and volatility, are observable as well. In practice, they are represented by the estimates obtained from the past data. In the process an "estimation" risk is introduced, implying that implicitly parameters are perceived as random (uncertain) quantities. This idea extends to the risk-neutral framework with a little tweak: although under the risk-neutral measure all assets grow at the same (interest) rate, which is obviously observable, the drift of the interest rate does not have to be. This dissertation is devoted to parameter uncertainty---one source of uncertainty that is often neglected and completely unrelated to the one associated with Brownian motion. We examine its implications in the context of: (1) pricing of corporate debt and equity; (2) valuation of real and financial call options, and (3) risk management. The first two belong to the class of American-style option-pricing problems*. As analytical solutions are impossible, we rely on numerical analysis, which proves that prices of both real and financial options are in fact higher than previously thought. Likewise equity is more valuable causing debt to be underpriced. These results are perfectly intuitive since option values are positively related to volatility while parameter uncertainty essentially increases the total uncertainty. The third application addresses the problem of a risk manager, who is uncertain about the true value of mean expected return, but must abide by constraints imposed by risk management procedures** such as portfolio insurance and value-at-risk control. Our findings indicate that: if constraint is relatively soft the investment strategy of a VAR-agent is more or less similar to that of an ordinary investor, although VAR-constraint appears to have reduced some of the potential risk-taking on behalf of the portfolio manager; in case VAR-constraint is too harsh, dynamic learning unequivocally strengthens risk aversion tendencies, so that the effect on asset prices may be very significant***.; *The timing of default in the first problem is considered endogenously chosen by the stockholders. **It seems that the very reason for some investors to rely on these procedures must be higher than usual uncertainty about environment, which can be interpreted as uncertainty about parameters. ***Surprisingly, we were able to calculate the composition of an optimal portfolio explicitly.