Portfolio risk estimation in volatile markets requires employing fat-tailed models for financial returns combined with copula functions to capture asymmetries in dependence and an appropriate downside risk measure. In this survey, we discuss how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and risk capital allocation with the average value-at-risk measure (AVaR). AVaR is the average loss provided that the loss is larger than a predefined value-at-risk level. We consider in some detail the AVaR calculation and estimation and investigate the stochastic stability.

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Applying real options thinking to company valuation seems theoretically and intuitively appealing. However, the real option analogy of a single European option as well as the compound option proxy perform poorly when applied to company valuation. We therefore suggest to rework the building blocks of real option applications to corporate valuation. We introduce a framework to delineate the distribution of the underlying asset in the risk neutral world, which is important in order to value any derivative. This is achieved by an algorithm to calibrate a basket option model using real world data of observed share prices. The fitting takes account of the class of stable distributions. The index of stability of asymmetric a stable distribution serves as an over-all parameter to characterise the specific distribution

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