Optimal portfolio selection and risk management: a comparison between the stable paretian approach and the Gaussian one

This paper analyzes stable paretian models in portfolio theory, risk management and option pricing theory. Firstly, we examine investor’s optimal choices when we assume respectively either Gaussian or stable non-Gaussian distributed index returns. Thus, we approximate discrete time optimal allocations assuming different distributional assumptions and considering several term structure scenarios. Secondly, we compare some stable approaches to compute VaR for heavy tailed return series. These models are subject to backtesting on out-of-sample data in order to assess their forecasting power. Finally, when asset prices are log-stable distributed, we propose a numerical valuation of option prices and we describe and compare delta hedging strategies when asset prices are either log-stable distributed or log-normal distributed.