Efficient Monte Carlo for Credit Derivatives under Factor-Copula Models

2006 ◽  
Author(s):  
Mike Curran
Keyword(s):  
Monte Carlo ◽  
Credit Derivatives ◽  
Copula Models

scholarly journals XVA PRINCIPLES, NESTED MONTE CARLO STRATEGIES, AND GPU OPTIMIZATIONS

2018 ◽  
Vol 21 (06) ◽  
pp. 1850030 ◽  
Author(s):  
LOKMAN A. ABBAS-TURKI ◽  
STÉPHANE CRÉPEY ◽  
BABACAR DIALLO
Keyword(s):  
Monte Carlo ◽  
Interest Rate ◽  
Outer Layer ◽  
Graphics Processing Units ◽  
Lower Layer ◽  
Credit Derivatives ◽  
Square Root ◽  
Root Number ◽  
Graphics Processing ◽  
Gpu Implementation

We present a nested Monte Carlo (NMC) approach implemented on graphics processing units (GPUs) to X-valuation adjustments (XVAs), where X ranges over C for credit, F for funding, M for margin, and K for capital. The overall XVA suite involves five compound layers of dependence. Higher layers are launched first, and trigger nested simulations on-the-fly whenever required in order to compute an item from a lower layer. If the user is only interested in some of the XVA components, then only the sub-tree corresponding to the most outer XVA needs be processed computationally. Inner layers only need a square root number of simulation with respect to the most outer layer. Some of the layers exhibit a smaller variance. As a result, with GPUs at least, error-controlled NMC XVA computations are doable. But, although NMC is naively suited to parallelization, a GPU implementation of NMC XVA computations requires various optimizations. This is illustrated on XVA computations involving equities, interest rate, and credit derivatives, for both bilateral and central clearing XVA metrics.

scholarly journals Dependent defaults and losses with factor copula models

2017 ◽  
Vol 5 (1) ◽  
pp. 375-399 ◽  
Author(s):  
Damien Ackerer ◽  
Thibault Vatter
Keyword(s):  
Term Structure ◽  
Credit Derivatives ◽  
Contingent Claims ◽  
High Dimensional ◽  
Loss Distribution ◽  
Copula Models ◽  
Special Cases ◽  
Static Factor ◽  
Standard Models ◽  
Key Features

Abstract We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with paircopula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of contingent claims can be exactly and efficiently computed when individual losses are discretely supported on a finite grid. Numerical examples study the key features affecting the loss distribution and multi-name credit derivatives prices. An empirical exercise illustrates the flexibility of our approach by fitting credit index tranche prices.

scholarly journals Quantifying Model Risk in Credit Derivatives Pricing

2018 ◽  
Author(s):  
Colin Turfus
Keyword(s):  
Monte Carlo ◽  
Interest Rate ◽  
Model Calibration ◽  
Good Accuracy ◽  
Credit Derivatives ◽  
Model Risk ◽  
Derivatives Pricing ◽  
Interest Rate Swap ◽  
The Impact ◽  
Rate Swap

We propose a methodology for the quantification of model risk in the context of credit derivatives pricing and CVA, where the uncertain or unmodelled parameter is often the correlation between rates and credit. We take the rates model to be Hull-White (normal) and the credit model to be Black-Karasinski (lognormal). We show how highly accurate analytic pricing formulae, hitherto unpublished, can be derived for CDS and extended to address instruments with defaultable Libor flows which may in addition be capped and/or floored. We also consider the pricing of a contingent CDS with an interest rate swap underlying. We derive explicit expressions showing how to good accuracy the dependence of model prices on the uncertain parameter(s) can be captured in analytic formulae which are readily amenable to computation without recourse to Monte Carlo or lattice-based computation. In so doing, we take into account the impact on model calibration of the uncertain (or unmodelled) parameter.

A new bivariate Archimedean copula with application to the evaluation of VaR

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Cigdem Topcu Guloksuz ◽  
Pranesh Kumar
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Simulation Method ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
General Motor ◽  
Copula Models ◽  
Bivariate Normal ◽  
Mc Simulation ◽  
Generator Function

AbstractIn this paper, a new generator function is proposed and based on this function a new Archimedean copula is introduced. The new Archimedean copula along with three representatives of Archimedean copula family which are Clayton, Gumbel and Frank copulas are considered as models for the dependence structure between the returns of two stocks. These copula models are used to simulate daily log-returns based on Monte Carlo (MC) method for calculating value at risk (VaR) of the financial portfolio which consists of two market indices, Ford and General Motor Company. The results are compared with the traditional MC simulation method with the bivariate normal assumption as a model of the returns. Based on the backtesting results, describing the dependence structure between the returns by the proposed Archimedean copula provides more reliable results over the considered models in calculating VaR of the studied portfolio.

Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
Author(s):  
Zdenek Sekanina
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Interplanetary Space ◽  
Porous Matrix ◽  
Maximum Diameter ◽  
Expansion Velocity ◽  
Solid Constituent ◽  
Meteoric Material ◽  
Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

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