We derive a formula for a Fourier transform of a counting process that describes the arrival of unpredictable events, and we show how this transform facilitates an analytical treatment of a range of valuation, hedging and risk management problems that arise in single name and portfolio credit risk. Example applications include reduced form pricing of credit sensitive securities referenced on si...

Coherent risk measures have lately become a hot topic in both theoretical research and practical applications. Since they possess a number of disadvantages, some generalizations and modifications have been proposed recently. In the present paper we propose one more generalization which holds a number of attractive properties. A representation theorem for the risk measures class has been obtaine...

We consider the class of concave distortion risk measures to study how choice is influenced by the decision-maker’s attitude to risk and provide comparative static results. We also assume ambiguity about the probability distribution of the risk and consider a framework à la Klibanoff, Marinacci, and Mukerji (2005) to study the value of information that resolves ambiguity. We show that this valu...

Banks and other financial institutions across the world use various approaches to quantify risk in their portfolios. Regulators require that value at risk (VaR), calculated based on the historical data, be used for certain reporting and capital allocation purposes. Currently, this simple risk measure, historical VaR or HsVaR, is computed by some firms using the full revaluation method, which is...

In this paper, we argue that there exists a distinction between risk measures and decision principles. Though both can be regarded as functionals assigning a real number to a random variable, we think that there is a hierarchy between the two concepts. Risk measures operate on the first “level”, quantifying the risk in the situation under consideration, while decision principles operate on the ...

We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of dynamic subscale invariant performance measures, on a general probability space, and discrete time setup. We prove a representation theorem of such measures...

We study a space of coherent risk measuresMφ obtained as certain expansions of coherent elementary basis measures. In this space, the concept of “Risk Aversion Function” φ naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give necessary and sufficient conditions on φ for Mφ to be a coherent measure. We find in this...

We propose a new method for constructing the hedge component in Merton’s ICAPM that uses a daily summary measure of economic activity to track time-varying investment opportunities. We then use nonparametric projections to compute a robust estimate of the conditional covariance between stock market returns and our daily economic activity index. We find that the new conditional covariance risk m...

The paper extends Diamond’s (1984) analysis of financial contracting with information asymmetry ex post and endogenous ”bankruptcy penalties” to allow for risk aversion of the borrower. The optimality of debt contracts, which Diamond obtained for the case of risk neutrality, is shown to be nonrobust to the introduction of risk aversion. This contrasts with the costly state verification literatu...

The No-Arbitrage model by Schonbucher [30] is combined with the Extended Vasicek Term Structure Model and applied to the pricing of DM-Eurobonds issued by sovereigns from emerging economies. Practical hedging according to the model is investigated. A portfolio of DM-Eurobonds is analyzed using the risk measures "Shortfall" and "Value at Risk".