Closed-form valuations of basket options using a multivariate normal inverse Gaussian model

Wu, Yang-Che; Liao, Szu-Lang; Shyu, So-De

doi:10.1016/j.insmatheco.2008.10.007

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…This model and its extensions are now widely used in finance (see, for example, Kumar et al (2011)). Its multivariate extension (Wu et al, 2009)) provides a basis for the spatiotemporal version. The multivariate normal inverse Gaussian distribution can be motivated as a scale mixture of Gaussian distributions.…”

Section: John Haslett Chaitanya Joshi and Vincent Garreta (Trinity Cmentioning

confidence: 99%

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Lindgren

Rue

Lindström

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

2,248

2,892

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Summary.Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorizing dense matrices is cubic in the dimension. Although computational power today is at an all time high, this fact seems still to be a computational bottleneck in many applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the precision matrix involved sparse, which enables the use of numerical algorithms for sparse matrices, that for fields in R 2 only use the square root of the time required by general algorithms. The specification of a GMRF is through its full conditional distributions but its marginal properties are not transparent in such a parameterization. We show that, using an approximate stochastic weak solution to (linear) stochastic partial differential equations, we can, for some GFs in the Matérn class, provide an explicit link , for any triangulation of R d , between GFs and GMRFs, formulated as a basis function representation. The consequence is that we can take the best from the two worlds and do the modelling by using GFs but do the computations by using GMRFs. Perhaps more importantly, our approach generalizes to other covariance functions generated by SPDEs, including oscillating and non-stationary GFs, as well as GFs on manifolds. We illustrate our approach by analysing global temperature data with a non-stationary model defined on a sphere.

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Section: John Haslett Chaitanya Joshi and Vincent Garreta (Trinity Cmentioning

confidence: 99%

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Lindgren

Rue

Lindström

2011

Journal of the Royal Statistical Society Series B: Statistical Methodology

2,248

2,892

View full text Add to dashboard Cite

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“…Therefore, in order to model asset returns it is possible to build an n-dimensional Lévy process whose increments follow an infinitely divisible NMV distribution by simply time-changing a multivariate Brownian motion with a common one-dimensional subordinator. While in Luciano and Schoutens (2006) and Tassinari and Corradi (2013) a model with independent Brownian motions was proposed, in Leoni and Schoutens (2008), Tassinari (2009), Wu et al (2009), Tassinari and Corradi (2014), Tassinari and Bianchi (2014), Bianchi et al (2016), and Bianchi and Tassinari (2020) correlated Brownian motions were considered. Furthermore, according to Frahm (2004), this family of distributions belongs to the class of elliptical variancemean mixtures.…”

Section: Normal Mean-variance Mixture Modelsmentioning

confidence: 99%

Multivariate non-Gaussian models for financial applications

Bianchi,

Hitaj,

Tassinari

2020

Preprint

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In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the properties of the dependence structure, and the computational tractability. For each model we analyze the main features, we provide the characteristic function, the marginal moments up to order four, the covariances and the correlations. Thus, we describe how to calibrate them on the time-series of log-returns with a view toward practical applications and possible numerical issues. To empirically compare these models, we conduct an analysis on a five-dimensional series of stock index log-returns.

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“…On the other hand, some other research has priced basket options whose asset dynamics are more appropriate to accommodate the empirical characteristics of the asset returns. Flamouris and Giamouridis (2007) priced basket options on assets following a Bernoulli jump-diffusion process using the Edgeworth expansion; Wu et al (2009) assumed that asset prices follow the multivariate normal inverse Gaussian model (mNIG) and employed the fast Fourier transform together with the methodology outlined by Milevsky and Posner (1998) to approximate the sum of assets following the mNIGs model as a mNIG; Xu and Zheng (2009) priced correlated local volatility jump-diffusion model deriving the Partial Integro Differential Equation (PIDE) driving the basket and approximating it via the asymptotic expansion method. Bae et al (2011) priced basket options (with positive weights) on assets following a jump-diffusion process by using the Taylor expansion method of Ju (2002).…”

Section: Existing Contributionsmentioning

confidence: 99%

Pricing and hedging basket options with exact moment matching

Leccadito

Paletta

Tunaru

2016

Insurance: Mathematics and Economics

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Theoretical models applied to option pricing should take into account the empirical characteristics of financial time series. In this paper, we show how to price basket options when the underlying asset prices follow a displaced log-normal process with jumps, capable of accommodating negative skewness and excess kurtosis. Our technique involves Hermite polynomial expansion that can match exactly the first m moments of the model-implied basket return. This method is shown to provide superior results for basket options not only with respect to pricing but also for hedging.

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Closed-form valuations of basket options using a multivariate normal inverse Gaussian model

Cited by 7 publications

References 14 publications

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach

Multivariate non-Gaussian models for financial applications

Pricing and hedging basket options with exact moment matching

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