2,810 research outputs found
Credit risk premia and quadratic BSDEs with a single jump
This paper is concerned with the determination of credit risk premia of
defaultable contingent claims by means of indifference valuation principles.
Assuming exponential utility preferences we derive representations of
indifference premia of credit risk in terms of solutions of Backward Stochastic
Differential Equations (BSDE). The class of BSDEs needed for that
representation allows for quadratic growth generators and jumps at random
times. Since the existence and uniqueness theory for this class of BSDEs has
not yet been developed to the required generality, the first part of the paper
is devoted to fill that gap. By using a simple constructive algorithm, and
known results on continuous quadratic BSDEs, we provide sufficient conditions
for the existence and uniqueness of quadratic BSDEs with discontinuities at
random times
Holomorphic transforms with application to affine processes
In a rather general setting of It\^o-L\'evy processes we study a class of
transforms (Fourier for example) of the state variable of a process which are
holomorphic in some disc around time zero in the complex plane. We show that
such transforms are related to a system of analytic vectors for the generator
of the process, and we state conditions which allow for holomorphic extension
of these transforms into a strip which contains the positive real axis. Based
on these extensions we develop a functional series expansion of these
transforms in terms of the constituents of the generator. As application, we
show that for multidimensional affine It\^o-L\'evy processes with state
dependent jump part the Fourier transform is holomorphic in a time strip under
some stationarity conditions, and give log-affine series representations for
the transform.Comment: 30 page
Cladding strategies for building-integrated photovoltaics
Photovoltaic cladding on the surfaces of commercial buildings has the potential for considerable reductions in carbon emissions due to embedded renewable power generation displacing conventional power utilization. In this paper, a model is described for the optimization of photovoltaic cladding densities on commercial building surfaces. The model uses a modified form of the ‘fill factor’ method for photovoltaic power supply coupled to new regression-based procedures for power demand estimation. An optimization is included based on a defined ‘mean index of satisfaction’ for matched power supply and demand (i.e., zero power exportation to the grid). The mean index of satisfaction directly translates to the reduction in carbon emission that might be expected over conventional power use. On clear days throughout the year, reductions of conventional power use of at least 60% can be achieved with an optimum cladding pattern targeted to lighting and small power load demands
Entropy of the Nordic electricity market: anomalous scaling, spikes, and mean-reversion
The electricity market is a very peculiar market due to the large variety of
phenomena that can affect the spot price. However, this market still shows many
typical features of other speculative (commodity) markets like, for instance,
data clustering and mean reversion. We apply the diffusion entropy analysis
(DEA) to the Nordic spot electricity market (Nord Pool). We study the waiting
time statistics between consecutive spot price spikes and find it to show
anomalous scaling characterized by a decaying power-law. The exponent observed
in data follows a quite robust relationship with the one implied by the DEA
analysis. We also in terms of the DEA revisit topics like clustering,
mean-reversion and periodicities. We finally propose a GARCH inspired model but
for the price itself. Models in the context of stochastic volatility processes
appear under this scope to have a feasible description.Comment: 16 pages, 7 figure
Evolutionary estimation of a Coupled Markov Chain credit risk model
There exists a range of different models for estimating and simulating credit
risk transitions to optimally manage credit risk portfolios and products. In
this chapter we present a Coupled Markov Chain approach to model rating
transitions and thereby default probabilities of companies. As the likelihood
of the model turns out to be a non-convex function of the parameters to be
estimated, we apply heuristics to find the ML estimators. To this extent, we
outline the model and its likelihood function, and present both a Particle
Swarm Optimization algorithm, as well as an Evolutionary Optimization algorithm
to maximize the likelihood function. Numerical results are shown which suggest
a further application of evolutionary optimization techniques for credit risk
management
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Optimal seismic upgrade timing in seaports with increasing throughput demand via real options
A real options (RO) formulation is proposed for decision-making on the timing to upgrade the seismic performance of existing seaports with increasing throughput demand in earthquake prone areas. The pay-off of the seismic upgrade investment option is estimated based on projected net earnings, repair cost, and downtime for a damaging reference seismic event having a pre-specified annual probability of occurrence. These projections inform a discrete-time RO binomial tree, following the American option valuation framework, which propagates the probability of the reference seismic event assuming Poisson temporal distribution of earthquake occurrence. The net present value of the expected annual payoff of the considered investment is used as an index supporting risk-informed decision-making discounted by the weighted average cost of capital (WACC). Numerical examples pertaining to decision makers with different capital cost, namely port authorities and terminal operators, operating in different economic environments typical of developed and developing countries are furnished to illustrate the applicability of the proposed RO formulation. It is found that high WACC and/or low throughput growth bring the optimal seismic upgrade timing forward, while earthquake consequences and upgrade cost have almost no influence on this timing
Liquidity risk premia : an empirical analysis of european corporate bond yields
In this study we highlight the importance of liquidity risk, especially in periods of market stress, and advocate in favour of an explicit consideration of a liquidity premium when using mark-to-model methodologies to value financial assets.
For European corporate bonds, we show that the liquidity premium, calculated as the difference between the yield spread of corporate bonds and the spread of credit default swaps, grew significantly during the recent market turmoil not only in absolute terms but also in relative terms. Although liquidity premiums were far from stable during the time frame of analysis-from 1 January 2005 to 31 December
2009 - on average roughly 40% of corporate yield spreads can be interpreted in terms of liquidity
premia.
We propose direct matching between the CDS and the underlying reference assets when computing liquidity premia. This differs from what seems to be the industry standard, which is simply to use indices when trying to infer market implied liquidity premia. Although computationally more demanding, the method we use is sounder from a theoretical point of view and produces richer results and analysis. With this method we are able present an analysis of liquidity risk premia per sector of activity
Derivatives and Credit Contagion in Interconnected Networks
The importance of adequately modeling credit risk has once again been
highlighted in the recent financial crisis. Defaults tend to cluster around
times of economic stress due to poor macro-economic conditions, {\em but also}
by directly triggering each other through contagion. Although credit default
swaps have radically altered the dynamics of contagion for more than a decade,
models quantifying their impact on systemic risk are still missing. Here, we
examine contagion through credit default swaps in a stylized economic network
of corporates and financial institutions. We analyse such a system using a
stochastic setting, which allows us to exploit limit theorems to exactly solve
the contagion dynamics for the entire system. Our analysis shows that, by
creating additional contagion channels, CDS can actually lead to greater
instability of the entire network in times of economic stress. This is
particularly pronounced when CDS are used by banks to expand their loan books
(arguing that CDS would offload the additional risks from their balance
sheets). Thus, even with complete hedging through CDS, a significant loan book
expansion can lead to considerably enhanced probabilities for the occurrence of
very large losses and very high default rates in the system. Our approach adds
a new dimension to research on credit contagion, and could feed into a rational
underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure
Affine term structure models : a time-changed approach with perfect fit to market curves
We address the so-called calibration problem which consists of fitting in a
tractable way a given model to a specified term structure like, e.g., yield or
default probability curves. Time-homogeneous jump-diffusions like Vasicek or
Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are
tractable processes but have limited flexibility; they fail to replicate actual
market curves. The deterministic shift extension of the latter (Hull-White or
JCIR++) is a simple but yet efficient solution that is widely used by both
academics and practitioners. However, the shift approach is often not
appropriate when positivity is required, which is a common constraint when
dealing with credit spreads or default intensities. In this paper, we tackle
this problem by adopting a time change approach. On the top of providing an
elegant solution to the calibration problem under positivity constraint, our
model features additional interesting properties in terms of implied
volatilities. It is compared to the shift extension on various credit risk
applications such as credit default swap, credit default swaption and credit
valuation adjustment under wrong-way risk. The time change approach is able to
generate much larger volatility and covariance effects under the positivity
constraint. Our model offers an appealing alternative to the shift in such
cases.Comment: 44 pages, figures and table
A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling
In this paper we propose a new nonparametric approach to interacting failing
systems (FS), that is systems whose probability of failure is not negligible in
a fixed time horizon, a typical example being firms and financial bonds. The
main purpose when studying a FS is to calculate the probability of default and
the distribution of the number of failures that may occur during the
observation period. A model used to study a failing system is defined default
model. In particular, we present a general recursive model constructed by the
means of inter- acting urns. After introducing the theoretical model and its
properties we show a first application to credit risk modeling, showing how to
assess the idiosyncratic probability of default of an obligor and the joint
probability of failure of a set of obligors in a portfolio of risks, that are
divided into reliability classes
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