This article outlines a few properties of the normal inverse gaussian distribution and demonstrates its ability to fit various shapes of smiles. Pdf the normal inverse gaussian distribution and the. 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. Comparison of parameter estimation methods for normal. Meanwhile we examine the price impact of the skewed nig distribution by adjusting the value of the two parameters. A quasimonte carlo algorithm for the normal inverse. 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. This paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. Browse other questions tagged probability derivatives inverse or ask your own question.
We show how the risk neutral dynamics can be obtained in this model, we interpret the effect of the riskneutralization, and we derive. Derivative of the inverse cumulative distribution function for the standard normal distribution. The normalinverse gaussian distribution nig is a continuous probability distribution that is. Modelling the volatility of financial assets using the normal inverse gaussian distribution. Normal inverse gaussian nig distribution which is a subclass of the generalized hyperbolic class of distributions has been successfully used in financial literature.
But in general, gamma and thus inverse gamma results are often accurate to a few epsilon, 14 decimal digits accuracy for 64bit double. The nig distribution was noted by blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by ole barndorffnielsen. Citeseerx the normal inverse gaussian distribution for. 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. Statistical analysis of model risk concerning temperature. 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 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.
Modelling the volatility of financial assets using the. American option pricing using garch models and the normal inverse gaussian distribution. Bernd schmid ralf werner 1st august 2005 abstract this paper presents an extension of the popular large homogeneous portfolio. The pricing is demonstrated on english and welsh males aged 65 in 20. 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. The nig distribution was noted by blaesild in 1977 as a. 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. Valuation of insurance products using a normal inverse. The normal inverse gaussian distribution can be generalised with a fifth parame ter to the socalled generalized inverse gaussian distributions. A few results related to vanilla options on rpi yearonyear inflation rates, as well as caplets on chf libor rates are exposed.
To achieve this we choose to work with the normal inverse gaussian distribution, which can accommodate both of these features. The normal inverse gaussian distribution is appropriate for this purpose because it exhibits. 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. Pdf the normal inverse gaussian distribution and the pricing of. 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. Normal inverse gaussian models are used in pricing derivatives and studies.
Creates research paper 200841 american option pricing. The main question this thesis answers is whether a normal inverse gaussian distribution performs. 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. So the fourier transforms of the gaussian function and its first and second order derivative are. In a riskneutral setting the application in a bs setting for the valuation of insurance products is tested. Comparison of parameter estimation methods for normal inverse. Drawdown measures and return moments international journal. 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. 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. Journal of derivatives, spring, 2007 abstract this paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. 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. Modeling and pricing longevity derivatives with stochastic.
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. Therefore we discuss this function in quite some detail in this chapter. Gaussian distribution and the pricing of derivatives. Discover a selection of our content to see how portfolio management research can directly benefit you. The authors propose the class of normal inverse gaussian nig distributions to approximate an unknown riskneutral density. Imposing the normal inverse gaussian distribution as the statistical model for the levy increments, we obtain a superior fit compared to the gaussian model when applied to spot price data from the oil and gas markets. Contingent claim pricing using a normal inverse gaussian. For someone who wants to pursue a career in credit derivatives, this is a recommendable reference book. American option pricing using garch models and the normal. Eberlein and keller 6 used a subfamily called the hyperbolic distributions to study. These are the moments that are important to many risk management applications. We model spot prices in energy markets with exponential nongaussian ornstein uhlenbeck processes.
Collateralized debt obligations pricing and factor models. The nig distribution is used by many studies for pricing options and stock price. The normal inverse gaussian distribution and the pricing of derivatives anders eriksson. The algorithm is based on a monte carlo technique found in rydberg, and is based on sampling three independent uniform variables. A parametrization in terms of sabr inputs is derived. The gaussian derivative function has many interesting properties. For each differentiation, a new factor hi wl is added. Drawdown measures and return moments international. In the rst chapter we introduce univariate gh distributions, construct an estimation.
The normal inverse gaussian distribution for synthetic cdo pricing anna kalemanova. 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. The moment matching method is used in estimating model parameters. Results indicate that the 2factor mbmm model gives the highest price for mortalityrelated type of contract. They create new, customized asset classes by allowing various investors to share. We consider the problem of pricing contingent claims using distortion oper ators. 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. The quantification of risk in norwegian stocks via the normal inverse gaussian distribution is studied. Garch models, normal inverse gaussian distribution, american options, least squares monte carlo method. In particular, improvements are found when considering the smile in implied standard deviations. Normalinverse gaussian distribution wikimili, the free. The appeal of the nig class of distributions is that it is characterized by the first four moments.
Normal inverse gaussian models are used in pricing derivatives and studies have reported superior performance of nig compared to gaussian models. Wang 2009 the normal inverse gaussian distribution and the pricing of derivatives, the journal of derivatives 16 3, 2337. 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. The normal inverse gaussian distribution and the pricing of. Creates research paper 200841 american option pricing using. Cdo, correlation smile, copula, factor model, large homogeneous portfolio, normal inverse gaussian. Pricing longevitylinked derivatives using a stochastic. 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 normal inverse gaussian distribution for synthetic. Sep 19, 2008 to achieve this we choose to work with the normal inverse gaussian distribution, which can accommodate both of these features. The normal inverse gaussian distribution and the pricing. 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. January 15, 2009 abstract we propose the class of normal inverse gaussian nig distributions to. Anna kalemanova, bernd schmid, ralf werner, the normal inverse gaussian distribution for synthetic cdo pricing, journal of derivatives 2007. The normal inverse gaussian distribution and the pricing of derivatives article pdf available in the journal of derivatives 163 august 2007 with 700 reads how we measure reads. Stentoft 2008 reports that nig modelling outperforms the gaussian case for pricing american options for three large us stocks. The normal inverse gaussian distribution for synthetic cdo. 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. 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. 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. This distribution was introduced in the finance literature recently and used together with garch models in, for example, barndorffnielsen, andersson, and jensen and lunde. We propose the class of normal inverse gaussian nig distributions to approximate an unknown risk neutral density.
Mortality rates, 2factor mbmm model, normal inverse gaussian distribution, longevitylinked derivatives. January 15, 2009 abstract we propose the class of normal inverse gaussian nig distributions to approximate an unknown risk neutral density. Modeling and pricing longevity derivatives with stochastic mortality using the esscher transform normal inverse gaussian l. Browse other questions tagged selfstudy normaldistribution matrix or ask your own question. Citeseerx document details isaac councill, lee giles, pradeep teregowda. This larger family was introduced in barndorffnielsen and halgreen 1977. The normal inverse gaussian distribution for synthetic cdo pricing.
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. This article proposes the normal inverse gaussian nig distribution as a more tractable alternative. The normal inverse gaussian distribution and the pricing of derivatives. Normal inverse gaussian distributions and stochastic. In this paper, we follow the philosophy in kalemanova et al 2007 and assess the pricing efficiency of both gaussian and normal inverse gaussian copula model during the turbulent market condition in 2008 and 2009. We apply the algorithm to three problems appearing in finance. 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. We propose a quasimonte carlo qmc algorithm to simulate variates from the normal inverse gaussian nig distribution.