Functional Asset Returns

Abstract

Discovering the price of a financial asset is a dynamic and complex process. Based on available literature and empirical evidence there is not singular approach of achieving such a task easily. Despite cur- rent advances in technology and in access to data, a general argument in favor of approaching this problem is centered on the information available at each moment of time for an individual financial asset. Accordingly, it seems coherent to use density functions as a reference for studying relevant aspects of asset prices and subsequently equity returns. Forecasts of density functions is an active approach in deci- sion theory and economics. The direction of my dissertation is related to the employment of density forecasting apply to asset prices.
Density forecasting may also may also of the interest for the manage- ment research areas since it provides more information than predic- tions produced considering only point and interval forecasts as these last frameworks yield limited sets of information.
Finding the correct true price density of a financial asset is as crucial as the characterization of it. This has implications for investors and managers in terms of both, risk management and value creation.
Despite, the acute of the underlying assumption made regarding the properties of the statistical distribution of the future asset fluctuation over time, finding the correct (true) price of a financial asset is as crucial as it is the characterization of it.
Regarding the literature that addresses alternative methods to fore- casts asset prices there are some papers that consider that one direct solution for modelling purposes will to assume that the time evolution of the asset price can be described by a random event over time. In this case, the method of choice to produce forecasts will be centered on the idea that the expected asset price will be a discrete process. An alternative discussion may be, to consider that the process that describes the path of the asset price is related to continuous fluctuations in space in which a diffusion process will have a central role. In general, my approach will be is centered on some equities traded on the S&P500. My approach is to forecast the density function of these values using functional time series relying on is principal component analysis (PCA).