• Dependence and Risk Management

    Simulating realistic correlation matrices for financial applications

    The major part of observed correlation matrices in financial applications exhibits the Perron-Frobenius property, namely a dominant eigenvector with only positive entries. We present a simulation algorithm for random correlation matrices satisfying this property, which can be augmented to take into account a realistic eigenvalue structure. From the construction principle applied in our algorithm, and the fact that it is able to generate all such correlation matrices, we are further able to compute explicitly the proportion of Perron-Frobenius correlation matrices in the set of all correlation matrices in a fixed dimension.

     

     

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  • Dependence and Risk Management

    Consistent iterated simulation of multivariate defaults

    A current market-practice to incorporate multivariate defaults in global risk-factor simulations is the iteration of (multiplicative) i.i.d. survival indicator increments along a given time-grid, where the indicator distribution is based on a copula ansatz. The underlying assumption is that the behavior of the resulting iterated default distribution is similar to the one-shot distribution. It is shown that in most cases this assumption is not fulfilled and furthermore numerical analysis is presented that shows sizable differences in probabilities assigned to both “survival-of-all” and “mixed default/survival” events. We furthermore present a survey of those copula families that make the aforementioned methodology work.

     

     

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  • Equity Derivatives

    A note on the modeling of quanto-converts (in German only)

    We discuss some critical aspects when evaluating convertible bonds whose underlying equity trades in a currency different from the bond currency.

     

     

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  • Dependence and Risk Management

    Portfolio selection based on graphs: does Mr. Markowitz have his finger in the pie?

    Some empirical studies suggest that the computation of certain graph structures from a (large) historical correlation matrix can be helpful in portfolio selection. In particular, a repeated finding is that information about the portfolio weights in the minimum variance portfolio (MVP) from classical Markowitz theory can be inferred from measurements of centrality in such graph structures. The present article compares the two concepts from a purely algebraic perspective. It is demonstrated that this heuristic relationship between graph centrality and the MVP is not inner-mathematical, at least not significantly strong. This means that empirically found relations between both concepts depend critically on the underlying historical data. Repeated empirical evidence for a strong relationship is hence shown to constitute a stylized fact of financial return time series, rather than the expected outcome of a heuristic similarity between both approaches.

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  • Credit Derivatives

    The negative basis conditioned on default

    The negative basis is an annualized earnings figure that measures the expected excess return of a bond investment over a reference discounting rate, after credit risk has been hedged away via credit default swap (CDS) protection. Unfortunately, the most appropriate measurement of the negative basis is in terms of a root of a non-trivial decreasing function. The goal of the present article is to derive closed proxy formulas for the negative basis, at least in special situations. Under the assumption that a credit event before maturity of bond (and CDS) is certain, i.e. conditioned on default before maturity, we are able to derive a very simple formula. Furthermore, a small enhancement of the formula provides a proxy formula for the (unconditional) negative basis. The availability of such closed formulas allows to study qualitative properties of the negative basis, such as dependence on the recovery rate assumption or leg prices

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