Normal inverse gaussian nig distribution which is a subclass of the generalized hyperbolic class of distributions has been successfully used in financial literature. 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 apply the algorithm to three problems appearing in finance. Garch models, normal inverse gaussian distribution, american options, least squares monte carlo method. We show how the risk neutral dynamics can be obtained in this model, we interpret the effect of the riskneutralization, and we derive. 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. The gaussian derivative function has many interesting properties.
Meanwhile we examine the price impact of the skewed nig distribution by adjusting the value of the two parameters. Gaussian distribution and the pricing of derivatives. 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. Browse other questions tagged probability derivatives inverse or ask your own question. 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.
Statistical analysis of model risk concerning temperature. 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 moment matching method is used in estimating model parameters. A few results related to vanilla options on rpi yearonyear inflation rates, as well as caplets on chf libor rates are exposed. But in general, gamma and thus inverse gamma results are often accurate to a few epsilon, 14 decimal digits accuracy for 64bit double. 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. The normal inverse gaussian distribution and the pricing of derivatives, the journal of derivatives, 16, 2337.
Wang 2009 the normal inverse gaussian distribution and the pricing of derivatives, the journal of derivatives 16 3, 2337. This larger family was introduced in barndorffnielsen and halgreen 1977. The normal inverse gaussian distribution and the pricing. These are the moments that are important to many risk management applications. Drawdown measures and return moments international journal. Creates research paper 200841 american option pricing. We propose the class of normal inverse gaussian nig distributions to approximate an unknown risk neutral 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. Discover a selection of our content to see how portfolio management research can directly benefit you. For someone who wants to pursue a career in credit derivatives, this is a recommendable reference book. The normal inverse gaussian distribution is appropriate for this purpose because it exhibits.
The normal inverse gaussian distribution and the pricing of. 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. Modeling and pricing longevity derivatives with stochastic mortality using the esscher transform normal inverse gaussian l. Valuation of insurance products using a normal inverse. This article outlines a few properties of the normal inverse gaussian distribution and demonstrates its ability to fit various shapes of smiles. 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 using. The quantification of risk in norwegian stocks via the normal inverse gaussian distribution is studied. Modelling the volatility of financial assets using the normal inverse gaussian distribution. Normal inverse gaussian models are used in pricing derivatives and studies have reported superior performance of nig compared to gaussian models. The main question this thesis answers is whether a normal inverse gaussian distribution performs. The nig distribution is used by many studies for pricing options and stock price.
Normalinverse gaussian distribution formulasearchengine. Bernd schmid ralf werner 1st august 2005 abstract this paper presents an extension of the popular large homogeneous portfolio. The normal inverse gaussian distribution and the pricing of derivatives. 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. Modelling the volatility of financial assets using the. 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. They create new, customized asset classes by allowing various investors to share.
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. 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. We propose a quasimonte carlo qmc algorithm to simulate variates from the normal inverse gaussian nig distribution. The normal inverse gaussian distribution can be generalised with a fifth parame ter to the socalled generalized inverse gaussian distributions. The normal inverse gaussian distribution for synthetic cdo. Collateralized debt obligations pricing and factor models. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Drawdown measures and return moments international. Pdf the normal inverse gaussian distribution and the pricing of. Normal inverse gaussian models are used in pricing derivatives and studies.
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. Citeseerx the normal inverse gaussian distribution for. The normal inverse gaussian distribution and the pricing of derivatives anders eriksson. Normalinverse gaussian distribution wikimili, the free. The nig distribution was noted by blaesild in 1977 as a. How to take derivative of multivariate normal density.
Sep 19, 2008 to achieve this we choose to work with the normal inverse gaussian distribution, which can accommodate both of these features. 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. Modeling and pricing longevity derivatives with stochastic. 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. The normal inverse gaussian distribution for synthetic cdo pricing anna kalemanova, bernd schmid, ralf werner the journal of derivatives feb 2007, 14 3 8094. To achieve this we choose to work with the normal inverse gaussian distribution, which can accommodate both of these features. January 15, 2009 abstract we propose the class of normal inverse gaussian nig distributions to approximate an unknown risk neutral density. The normal inverse gaussian distribution for synthetic. Comparison of parameter estimation methods for normal. The employment of the nig distribution not only speeds up the computation time significantly but also brings more flexibility into the dependence structure.
Therefore we discuss this function in quite some detail in this chapter. The normalinverse gaussian distribution nig is a continuous probability distribution that is. We model spot prices in energy markets with exponential nongaussian ornstein uhlenbeck processes. 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. In particular, improvements are found when considering the smile in implied standard deviations. 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. A parametrization in terms of sabr inputs is derived. Mortality rates, 2factor mbmm model, normal inverse gaussian distribution, longevitylinked derivatives. Results indicate that the 2factor mbmm model gives the highest price for mortalityrelated type of contract. 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. Derivative of the inverse cumulative distribution function for the standard normal distribution. The algorithm is based on a monte carlo technique found in rydberg, and is based on sampling three independent uniform variables. 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.
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. 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. Browse other questions tagged selfstudy normaldistribution matrix or ask your own question. The normal inverse gaussian distribution for synthetic cdo pricing. Comparison of parameter estimation methods for normal inverse. Contingent claim pricing using a normal inverse gaussian. Pdf the normal inverse gaussian distribution and the. Cdo, correlation smile, copula, factor model, large homogeneous portfolio, normal inverse gaussian. 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. A quasimonte carlo algorithm for the normal inverse. This distribution was introduced in the finance literature recently and used together with garch models in, for example, barndorffnielsen, andersson, and jensen and lunde.
Eberlein and keller 6 used a subfamily called the hyperbolic distributions to study. Normal inverse gaussian distributions and stochastic. The authors propose the class of normal inverse gaussian nig distributions to approximate an unknown riskneutral density. We consider the problem of pricing contingent claims using distortion oper ators. 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. American option pricing using garch models and the normal. 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. Stentoft 2008 reports that nig modelling outperforms the gaussian case for pricing american options for three large us stocks. The nig distribution was noted by blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by ole barndorffnielsen.
Journal of derivatives, spring, 2007 abstract this paper presents an extension of the popular large homogeneous portfolio lhp approach to the pricing of cdos. The normal inverse gaussian distribution for synthetic cdo pricing anna kalemanova. 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. Anna kalemanova, bernd schmid, ralf werner, the normal inverse gaussian distribution for synthetic cdo pricing, journal of derivatives 2007. Pricing longevitylinked derivatives using a stochastic. So the fourier transforms of the gaussian function and its first and second order derivative are. American option pricing using garch models and the normal inverse gaussian distribution. The appeal of the nig class of distributions is that it is characterized by the first four moments. The pricing is demonstrated on english and welsh males aged 65 in 20. In the rst chapter we introduce univariate gh distributions, construct an estimation.
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