The normal inverse gaussian distribution and the pricing of derivatives

Therefore we discuss this function in quite some detail in this chapter. In the rst chapter we introduce univariate gh distributions, construct an estimation. The normal inverse gaussian distribution and the pricing of derivatives, the journal of derivatives, 16, 2337. Normal inverse gaussian nig distribution which is a subclass of the generalized hyperbolic class of distributions has been successfully used in financial literature. Modeling and pricing longevity derivatives with stochastic. Statistical analysis of model risk concerning temperature. They create new, customized asset classes by allowing various investors to share. The nig distribution is used by many studies for pricing options and stock price. Normalinverse gaussian distribution formulasearchengine. The employment of the nig distribution not only speeds up the computation time significantly but also brings more flexibility into the dependence structure. Drawdown measures and return moments international. This paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. For each differentiation, a new factor hi wl is added. January 15, 2009 abstract we propose the class of normal inverse gaussian nig distributions to.

Derivative of the inverse cumulative distribution function for the standard normal distribution. In particular, improvements are found when considering the smile in implied standard deviations. Mortality rates, 2factor mbmm model, normal inverse gaussian distribution, longevitylinked derivatives. The normal inverse gaussian distribution and the pricing of. We propose a quasimonte carlo qmc algorithm to simulate variates from the normal inverse gaussian nig distribution. Wang 2009 the normal inverse gaussian distribution and the pricing of derivatives, the journal of derivatives 16 3, 2337. January 15, 2009 abstract we propose the class of normal inverse gaussian nig distributions to approximate an unknown risk neutral density. The main question this thesis answers is whether a normal inverse gaussian distribution performs. Written in a very practical way, the technical contents of the book should not be too difficult to follow for a reader with intermediate quantitative skills. For someone who wants to pursue a career in credit derivatives, this is a recommendable reference book. The quantification of risk in norwegian stocks via the normal inverse gaussian distribution is studied. Collateralized debt obligations pricing and factor models. 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. This article proposes the normal inverse gaussian nig distribution as a more tractable alternative.

Discover a selection of our content to see how portfolio management research can directly benefit you. The nig distribution was noted by blaesild in 1977 as a. One strength of this approach is that the authors link the pricing of individual derivatives to the moments of the riskneutral distribution, which has an intuitive. The algorithm is based on a monte carlo technique found in rydberg, and is based on sampling three independent uniform variables. We model spot prices in energy markets with exponential nongaussian ornstein uhlenbeck processes. In this paper we propose a feasible way to price american options in a model with time varying volatility and conditional skewness and leptokurtosis using garch processes and the normal inverse gaussian distribution. The authors propose the class of normal inverse gaussian nig distributions to approximate an unknown riskneutral density. Results indicate that the 2factor mbmm model gives the highest price for mortalityrelated type of contract. The normal inverse gaussian distribution is appropriate for this purpose because it exhibits. Normal inverse gaussian models are used in pricing derivatives and studies. We consider the problem of pricing contingent claims using distortion oper ators.

This distribution was introduced in the finance literature recently and used together with garch models in, for example, barndorffnielsen 1997, andersson 2001, and jensen and lunde 2001. Drawdown measures and return moments international journal. Cdo, correlation smile, copula, factor model, large homogeneous portfolio, normal inverse gaussian. Pdf the normal inverse gaussian distribution and the. The normal inverse gaussian distribution and the pricing of derivatives. American option pricing using garch models and the normal inverse gaussian distribution. A parametrization in terms of sabr inputs is derived. Pdf the normal inverse gaussian distribution and the pricing of. The nig distribution was noted by blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by ole barndorffnielsen. Comparison of parameter estimation methods for normal inverse. The normal inverse gaussian distribution for synthetic cdo pricing.

Normalinverse gaussian distribution wikimili, the free. 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. Anna kalemanova, bernd schmid, ralf werner, the normal inverse gaussian distribution for synthetic cdo pricing, journal of derivatives 2007. Modelling the volatility of financial assets using the normal inverse gaussian distribution. The appeal of the nig class of distributions is that it is characterized by the first four moments. Meanwhile we examine the price impact of the skewed nig distribution by adjusting the value of the two parameters. Creates research paper 200841 american option pricing using. Comparison tests on several standard cds index portfolios show that the nig distribution has better tail characteristics than the normal and it is much more efficient for large scale computations than the multivariate student t. Comparison of parameter estimation methods for normal. The normal inverse gaussian distribution for synthetic. Stentoft 2008 reports that nig modelling outperforms the gaussian case for pricing american options for three large us stocks. A quasimonte carlo algorithm for the normal inverse.

Browse other questions tagged probability derivatives inverse or ask your own question. But in general, gamma and thus inverse gamma results are often accurate to a few epsilon, 14 decimal digits accuracy for 64bit double. Citeseerx the normal inverse gaussian distribution for. The pricing is demonstrated on english and welsh males aged 65 in 20. Modeling and pricing longevity derivatives with stochastic mortality using the esscher transform normal inverse gaussian l. So the fourier transforms of the gaussian function and its first and second order derivative are. Browse other questions tagged selfstudy normaldistribution matrix or ask your own question. Garch models, normal inverse gaussian distribution, american options, least squares monte carlo method. These are the moments that are important to many risk management applications.

Sep 01, 2012 the normal inverse gaussian distribution and non gaussian blackscholes contingent pricing the nig distribution is a member of the wider class of generalized hyperbolic distributions. To achieve this we choose to work with the normal inverse gaussian distribution, which can accommodate both of these features. This paper discusses european style option pricing for both path dependent and nonpath dependent cases where the log returns of the underlying asset follow the normal inverse gaussian nig distributions. A few results related to vanilla options on rpi yearonyear inflation rates, as well as caplets on chf libor rates are exposed.

Journal of derivatives, spring, 2007 abstract this paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. Creates research paper 200841 american option pricing. Bernd schmid ralf werner 1st august 2005 abstract this paper presents an extension of the popular large homogeneous portfolio. Valuation of insurance products using a normal inverse. Bolviken and benth 2000 examine seven stocks in the norwegian stock exchange and one stock in the new york stock exchange using the nig model, and report that nig outperforms the gaussian model. Sep 19, 2008 to achieve this we choose to work with the normal inverse gaussian distribution, which can accommodate both of these features. We propose the class of normal inverse gaussian nig distributions to approximate an unknown risk neutral density. American option pricing using garch models and the normal. The normal inverse gaussian distribution can be generalised with a fifth parame ter to the socalled generalized inverse gaussian distributions. The gaussian derivative function has many interesting properties. This larger family was introduced in barndorffnielsen and halgreen 1977.

The normal inverse gaussian distribution for synthetic cdo pricing anna kalemanova, bernd schmid, ralf werner the journal of derivatives feb 2007, 14 3 8094. How to take derivative of multivariate normal density. For fixed values of a, 11 and the class of normal inverse gaussian distributions constitutes an exponential model with 3 as canonical parameter and x as canonical statistic. 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. The normal inverse gaussian distribution and the pricing. Eberlein and keller 6 used a subfamily called the hyperbolic distributions to study. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The normal inverse gaussian distribution for synthetic cdo. Lhp which has already become a standard model in practice assumes a flat default correlation structure over the reference credit portfolio and models defaults using a one factor gaussian. In order to derive some explicit results we focus our analysis on two examples of a hyperbolic family of distributions, namely variancegamma and normalinverse gaussian, two distribution functions used in the area of pricing financial derivatives. One strength of our approach is that we link the pricing of individual derivatives to the moments of the risk neutral distribution, which has an intuitive appeal in. One strength of this approach is that the authors link the pricing of individual derivatives to the moments of the riskneutral distribution, which has an intuitive appeal in terms of how volatility, skewness, and kurtosis of the riskneutral distribution can explain the behavior of derivative prices.

We show how the risk neutral dynamics can be obtained in this model, we interpret the effect of the riskneutralization, and we derive. The normal inverse 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. The normal inverse gaussian distribution and the pricing of derivatives anders eriksson, eric ghysels, fangfang wang the journal of derivatives feb 2009, 16 3 2337. In order to derive some explicit results we focus our analysis on two examples of a hyperbolic family of distributions, namely variancegamma and normal inverse gaussian, two distribution functions used in the area of pricing financial derivatives. This distribution was introduced in the finance literature recently and used together with garch models in, for example, barndorffnielsen, andersson, and jensen and lunde. This article outlines a few properties of the normal inverse gaussian distribution and demonstrates its ability to fit various shapes of smiles. In a riskneutral setting the application in a bs setting for the valuation of insurance products is tested. Contingent claim pricing using a normal inverse gaussian. Modelling the volatility of financial assets using the. The normalinverse gaussian distribution nig is a continuous probability distribution that is. Gaussian distribution and the pricing of derivatives.

Erik bolviken, fred espen beth, quantification of risk in norwegian stocks via the normal inverse gaussian distribution, proceedings of the afir 2000 colloquium anna kalemanova, bernd schmid, ralf werner, the normal inverse gaussian distribution for synthetic cdo pricing, journal of derivatives 2007. 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 moment matching method is used in estimating model parameters. Normal inverse gaussian distributions and stochastic. 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 published the.