• Dependence and Risk Management

    Portfolio optimization for credit-risky assets under extreme dependence

    We consider power utility maximization in a multivariate Black-Scholes model that is enhanced by credit risk via the Marshall-Olkin exponential distribution. On the practical side, the model is analytically tractable, easy to interpret, and thus simple to implement. On the theoretical side, the model constitutes a well-justified and intuitive mathematical wrapping to study the effect of extreme and higher-order dependence on optimal portfolios. In particular, we show that it is rich enough to model both, situations in which diversification is beneficial and situations in which this is not the case.

     

     

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  • Equity Derivatives

    Improved analytical proxy formulas for convertible bonds

    In a previous article, we derived a sharp analytical lower bound for the price of a convertible bond. When a soft call covenant was present, a lower bound could only be derived in a simple credit-equity model, and two simplifying assumptions were made: (1) the soft call right may be executed at any time, starting at time t=0, and (2) the bond and its underlying equity are denominated in the same currency. This addendum summarizes the necessary adjustments to the formula in order to get rid of these restrictive assumptions.

     

     

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  • Equity Derivatives

    Integrated convertibles - Investment styles and characteristics integration applied to convertible bonds

    This article explores six investment styles like momentum, value, defensive and others in the niche asset class of US convertible bonds. While only carry and a characteristics integration approach yield promising results, it seems that both strategies can be explained by common equity and bond market factors. Thus, the case of characteristics investing in convertible bonds is not as strong as in other more traditional asset classes. However, convertible bond characteristics integration provides an interesting opportunity to get exposure to equity and bond markets as well as to multiple characteristics at once.

     

     

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  • Dependence and Risk Management

    Geostatistical modeling of financial data

    We explore how the joint modeling of financial assets can utilize methodologies from geostatistical modeling. The considered approach is essentially based on modeling data as realizations of a (Gaussian) random field. This allows for a parsimonious representation of the dependence structure by means of a covariance function taken to be a function of the distance between observations. A key beneft of this ansatz is the possibility to include new data points, i.e. to consider new companies in financial applications. Consequently, geostatistical modeling has appealing benefits in the contexts of covariance matrix estimation and missing data imputation. We thoroughly discuss the necessary adjustments when applying geostatistical methods to the high-dimensional framework that entails the modeling of financial data, instead of the 2D/3D coordinate space encountered in original applications of the method. We illustrate the two use cases of covariance matrix estimation and missing data imputation on a data set of CDS spreads of constituents of the iTraxx universe.

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  • Credit Derivatives

    Static pricing-hedging duality for credit default swaps and the negative basis arbitrage

    Assuming the absence of arbitrage in a single-name credit risk model, it is shown how to replicate the risk-free bank account until a credit event by a static portfolio of a bond and infinitely many credit default swaps (CDS). From the viewpoint of classical arbitrage pricing theory this static portfolio can be viewed as the solution of a credit risk hedging problem whose dual problem is to price the bond consistently with the CDS. This duality is maintained when the risk-free rate is shifted parallelly. In practice, there is a unique parallel shift that is consistent with observed market prices for bond and credit default swaps. The resulting, risk-free trading strategy in case of a positive shift earns more than the risk-free rate, is referred to as negative basis arbitrage in the market, and the parallel shift defined in this way is a scientifically well-justified definition for what the market calls negative basis. In economic terms, it is a premium for taking the un-modeled residual risks of a bond investment after interest rate risk and credit risk are hedged away, predominantly these are liquidity risk and legal risk.

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