Information Asymmetry in Pricing of Credit Derivatives

We study the pricing of credit derivatives with asymmetric information. The managers have complete information on the value process of the firm and on the default threshold, while the investors on the market have only partial observations, especially about the default threshold. Different information structures are distinguished using the framework of enlargement of filtrations. We specify risk neutral probabilities and we evaluate default sensitive contingent claims in these cases

Comparison of insiders’ optimal strategies depending on the type of side-information

AbstractIn this paper, we consider a complete continuous-time financial market with discontinuous prices and different types of side-information (initial or progressive strong information, weak information). The agents strive to maximize the expectation of the logarithm of their terminal wealth. Our purpose is to explicit and to simulate the optimal strategy of the insiders in some examples of side-information. We compare those optimal strategies, depending on the type of side-information

Ramsey Rule with Progressive utility and Long Term Affine Yields Curves

The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.Comment: arXiv admin note: substantial text overlap with arXiv:1404.189

Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial. Thus, after recalling some important properties on progressive utility, this paper first provides an extension of the notion of a consistent progressive utility to a consistent pair of progressive utilities of investment and consumption. An optimality condition is that the utility from the wealth satisfies a second order SPDE of HJB type involving the Fenchel-Legendre transform of the utility from consumption. This SPDE is solved in order to give a full characterization of this class of consistent progressive pair of utilities. An application of this results is to revisit the classical backward optimization problem in the light of progressive utility theory, emphasizing intertemporal-consistency issue. Then we study the dynamics of the marginal utility yield curve, and give example with backward and progressive power utilities

Credit Risk with asymmetric information on the default threshold

International audienceWe study the impact of asymmetric information in a general credit model where the default is triggered when a fundamental diff usion process of the firm passes below a random threshold. Inspired by some recent technical default events during the fi nancial crisis, we consider the role of the firm's managers who choose the level of the default threshold and have complete information. However, other investors on the market only have partial observations either on the process or on the threshold. We specify the accessible information for di fferent types of investors. Besides the framework of progressive enlargement of fi ltrations usually adopted in the credit risk modelling, we also combine the results on initial enlargement of filtrations to deal with the uncertainty on the default threshold. We consider several types of investors who have di fferent information levels and we compute the default probabilities in each case. Numerical illustrations show that the insiders who have extra information on the default threshold obtain better estimations of the default probability compared to the standard market investors

Explicit correlations for the Hawkes processes

In this paper we fill a gap in the literature by providing exact and explicit expressions for the correlation of general Hawkes processes together with its intensity process. Our methodology relies on the Poisson imbedding representation and on recent findings on Malliavin calculus and pseudo-chaotic representation for counting processes

Information Asymmetry in Pricing of Credit Derivatives

We study the pricing of credit derivatives with asymmetric information. The managers have complete information on the value process of the firm and on the default threshold, while the investors on the market have only partial observations, especially about the default threshold. Different information structures are distinguished using the framework of enlargement of filtrations. We specify risk neutral probabilities and we evaluate default sensitive contingent claims in these cases.

Optimal stopping contract for Public Private Partnerships under moral hazard

This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, in continuous-time and with a continuous payment, with the possibility for the public to stop the contract. The public ("she") pays a continuous rent to the consortium ("he"), while the latter gives a best response characterized by his effort. This effect impacts the drift of the social welfare, until a terminal date decided by the public when she stops the contract and gives compensation to the consortium. Usually, the public can not observe the effort done by the consortium, leading to a principal agent's problem with moral hazard. We solve this optimal stochastic control with optimal stopping problem in this context of moral hazard. The public value function is characterized by the solution of an associated Hamilton Jacobi Bellman Variational Inequality. The public value function and the optimal effort and rent processes are computed numerically by using the Howard algorithm. In particular, the impact of the social welfare's volatility on the optimal contract is studied

Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges

This article investigates the latest developments in longevity risk modelling, and explores the key risk management challenges for both the financial and insurance industries. The article discusses key definitions that are crucial for the enhancement of the way longevity risk is understood; providing a global view of the practical issues for longevity-linked insurance and pension products that have evolved concurrently with the steady increase in life expectancy since 1960s. In addition, the article frames the recent and forthcoming developments that are expected to action industry-wide changes as more effective regulation, designed to better assess and efficiently manage inherited risks, is adopted. Simultaneously, the evolution of longevity is intensifying the need for capital markets to be used to manage and transfer the risk through what are known as Insurance-Linked Securities (ILS). Thus, the article will examine the emerging scenarios, and will finally highlight some important potential developments for longevity risk management from a financial perspective with reference to the most relevant modelling and pricing practices in the banking industry.Longevity Risk ; securitization ; risk transfer ; incomplete market ; life insurance ; stochastic mortality ; pensions ; long term interest rate ; regulation ; population dynamics