Defaultable claims

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  • Throughout this paper, we consider a valuation method for contingent claims taking control of shortfall risk into account in the framework of complete market models. After giving a general form of the valuation, we shall deal with models whose underlying assets are described by diffusion processes, and obtain a result for American type claims.

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  • A considerable part of the vast development in Mathematical Finance over the last two decades was determined by the application of stochastic methods. These were therefore chosen as the focus of the 2003 School on “Stochastic Methods in Finance”. The growing interest of the mathematical community in this field was also reflected by the extraordinarily high number of applications for the CIME-EMS School. It was attended by 115 scientists and researchers, selected from among over 200 applicants. The attendees came from all continents: 85 were Europeans, among them 35 Italians.

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  • In this paper we develop a contingent valuation model for zero-coupon bonds with de- fault. In order to emphasize the role of maturity time and place of the lender’s claim in the hierarchy of debt of a Þrm, we consider a Þrm that issues two bonds with different ma- turities and different seniorage. The model allows us to analyze the implications of both debt renegotiation and capital structure of a Þrm on the prices of bonds.

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  • Overall, the rapid development in the market for credit risk transfer played a major role altering banks’ functions. Structurally, securitization allowed banks to turn traditionally illiquid claims (overwhelmingly in the form of bank loans) into marketable securities. The development of securitization has therefore allowed banks to off-load part of their credit exposure to other investors thereby lowering regulatory pressures on capital requirements allowing them to raise new funds.

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  • In modern nancial systems, an intricate web of claims and obligations links the balance sheets of a wide variety of intermediaries, such as banks and hedge funds, into a network structure. The advent of sophisticated nancial products, such as credit default swaps and collateralised debt obligations, has heightened the complexity of these balance sheet connections still further.

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  • This paper models two key channels of contagion in nancial systems by which default may spread from one institution to another. The primary focus is on how losses can potentially spread via the complex network of direct counterparty exposures following an initial default. But, as Cifuentes et al (2005) and Shin (2008) stress, the knock-on effects of distress at some nancial institutions on asset prices can force other nancial entities to write down the value of their assets, and we also model the potential for this effect to trigger further rounds of default.

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  • In what follows, we construct a simple nancial system involving entities with interlocking balance sheets and use these techniques to model the spread and probability of contagious default following an unexpected shock, analytically and numerically. Unlike the generic, undirected graph model of Watts (2002), our model provides an explicit characterisation of balance sheets, making clear the direction of claims and obligations linking nancial institutions. It also includes asset price interactions with balance sheets, allowing the effects of asset-side contagion to be clearly delineated.

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  • A convertible bond is a security that the holder can convert into a specified number of underlying shares. We enrich the standard model by introducing some default risk of the issuer. Once default has occured payments stop immediately. In the context of a reduced form model with infinite time horizon driven by a Brownian motion, analytical formulae for the no-arbitrage price of this American contingent claim are obtained and characterized in terms of solutions of free boundary problems.

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  • In this paper we provide a formalization of a set of default rules that we claim are required for the transfer of information such as causation, event rate and duration in the interpretation of metaphor. Such rules are domain-independent and are identified as invariant adjuncts to any conceptual metaphor. We also show a way of embedding the invariant mappings in a semantic framework.

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