The normal inverse gaussian distribution for synthetic cdo pricing

The normal inverse gaussian distribution nig is a mixture of normal and inverse gaussian distributions. Recently, geng xu 10 used the mixture copula model of multigaussian distributions and dezhong wang 11 used double mixture of t and gaussian copula to price the cdo tranches, and. The nig distribution was noted by blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by ole barndorffnielsen, in the next year barndorffnielsen. The nig distribution was noted by blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by ole barndorffnielsen, in. Lhp which has already become a standard model in practice assumes a flat default correlation structure over the reference credit portfolio and models. On the mechanism of cdos behind the current financial. Synthetic cdo pricing using the double normal inverse gaussian copula with stochastic factor loadings diploma thesis submitted to the eth zurich and university of zurich for the degree of master of advanced studies in finance presented by annelis luscher supervisor. Houdain june 2005 abstract the reported correlation smile in the cdo market is proof that the spreads of cdos tranches are not consistent when we use the widelyknown gaussian onefactor model for the pricing. In order to obtain the fair premium of the cdo tranche, the market standard pricing modelone factor gaussian copula model, and its various extension models e. With the exception of the gaussian distribution, one. We consider examples with fat tailed distributions, stochastic and local correlation which generally provide a closer fit to market quotes. Mcneil department of mathematics eth zurich december 2005. Bernd schmid ralf werner 1st august 2005 abstract this paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. Sorry, we are unable to provide the full text but you may find it at the following locations.

This book describes the stateoftheart in quantitative and computational modelling of cdos. January 15, 2009 abstract we propose the class of normal inverse gaussian nig distributions to. Vasicek, probability of loss on a loan portfolio, working paper, kmv published in risk, december 2002 with the. The normal tempered stable distribution for synthetic cdo pricing working paper philipp ehrler dr. A synthetic cdo is a pool of cds, of which the cumulative loss on the pool is divided into di. Anna kalemanova bernd schmid ralf werner august 2005 risklab germany gmbh nymphenburger str.

These models are extensions of the classic single factor gaussian copula and may generate a skew. Meanwhile we examine the price impact of the skewed nig distribution by adjusting the value of the two parameters. The normal inverse gaussian distribution for synthetic cdo pricing anna kalemanova. So if you want to know which of your data lie outside the normal 95% confidence interval, and you have their zscores, first calculate the zscore for a pvalue of 0. Besides speeding up mc simulations, the major advantage of increment techniques is their ability to handle large. This paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. The expected losses on a tranche can be estimated from the default distribution of the reference portfolio. February 28, 2007, 14 3 the journal of derivatives. In probability theory, the inverse gaussian distribution also known as the wald distribution is a twoparameter family of continuous probability distributions with support on 0. The normal inverse gaussian distribution and the pricing of derivatives anders eriksson. Pricing synthetic cdo tranches pricing a cdo tranche is a function of the tranches notional, spread, and expected default losses.

One of the major reasons was the complexity of cdo structure and the existence of skewness in correlation among tranches. The normal inverse gaussian distribution for synthetic cdo pricing article pdf available in the journal of derivatives 143. The first part of the paper shows a brief introduction of synthetic cdo pricing method. Yang, pricing cdo tranches in an intensitybased model with the meanreversion app roach, working paper, swansea university, 2009. P values for normal inverse gaussian distribution matlab. The normal inverse gaussian distribution for synthetic cdo pricing anna kalemanova, bernd schmid, ralf werner the journal of derivatives feb 2007, 14 3 8094. This paper addresses the pricing of the most tradable type of multiname credit derivatives, synthetic cdo, via a newly introduced model based on a mixture copula model obtained by combining the normal inverse gaussian nig distribution with a gaussian one which will result in the mgnig. Loss distribution generation in credit portfolio modeling. Normalinverse gaussian distribution formulasearchengine. After presenting some basic facts of the latter in section 1.

The normal inverse gaussian distribution for synthetic cdo. The normal inverse gaussian distribution and the pricing. Cdo2 pricing using gaussian mixture model with transformation of loss distribution. The normalinverse gaussian distribution nig is continuous probability distribution that is defined as the normal variancemean mixture where the mixing density is the inverse gaussian distribution. The normal inverse gaussian distribution for synthetic cdo pricing. Cdo squared pricing using gaussian mixture model with. A new methodology using normal inverse gaussian distributions. In this work we present an analysis of cdo pricing models with a focus on correlation skew models. We present a new approach to price cdo squaredtype transactions consistently with the pricing of the underlying cdos. The nig distribution was noted by blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by ole barndorffnielsen. Continuous setting and gaussian generalized lambda distribution model for synthetic cdo pricing abstract pricing cdo has been a very challenging task to both researchers and practitioners. Pricing cdo tranches in an intensity based model with the.

Werner 2007 the normal inverse gaussian distribution for synthetic cdo pricing, the journal of derivatives 14 3, 8094. The normal tempered stable distribution for synthetic cdo. Wernerthe normal inverse gaussian distribution for synthetic cdo pricing journal of derivatives, 14 3 2007, pp. But in general, gamma and thus inverse gamma results are often accurate to a few epsilon, 14 decimal digits accuracy for 64bit double. Li, michael liang quantitative analytics global credit derivatives barclays capital 200 park ave new york, ny 10166 september 5, 2005 abstract we present a new approach to price cdo. Montecarlo methods for the valuation of synthetic cdo. Validation of normal inverse gaussian distribution for. Increment variance reduction techniques are addons to monte carlo mc simulations. The purpose of the inverse gaussian distribution is to generate zscores also known as critical values from p values for the purpose of calculating confidence intervals for a given probability. Kendall 1945 the treatment of ties in ranking problems, biometrika 33. The normalinverse gaussian distribution nig is a continuous probability distribution that is defined as the normal variancemean mixture where the mixing density is the inverse gaussian distribution.

This paper follows kalemanova et al 2007 and assesses the pricing efficiency of both onefactor gaussian copula model the normal inverse gaussian nig copula model during the turbulent market condition by using data in 2008 and 2009. Home browse by title periodicals mathematical and computer modelling. Cdo pricing using single factor mgnig copula model with. Drawdown measures and return moments international. Anna kalemanovas 3 research works with 148 citations and 463 reads, including. A comparative analysis of correlation skew modeling.

We first present an extension to the current market standard model using a gaussian mixture gm copula model. Collateralized debt obligation cdo modelling comparisons. Continuous setting and gaussian generalized lambda. They make mc simulations converging faster by repeating the number of simulations with an incremental rate derived from mathematical functions. Credit derivatives have enjoyed explosive growth in the last decade, particularly synthetic collateralised debt obligations synthetic cdos. Journal of derivatives, spring, 2007 abstract this paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. With the cdo pricing library for premia, we initialize a onefactor gaussian copula with parameter. Collateralized debt obligations pricing and factor models. How to determine the default loss distribution of the whole credit portfolio is the most critical part for pricing cdos. Synthetic cdo pricing using the double normal inverse. Cdo pricing using single factor m gni g copula model with stochastic correlation and random factor loading. Gaussian such as clayton, student t, double t, nig, etc. In advances in mathematical finance applied and numerical harmonic analysis 259278.