Application of Bernstein Copulas to the Pricing of Multi-Asset Derivatives

Tavin, Bertrand

doi:10.1007/978-3-642-35407-6_13

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…•, • µ ⊥ . Note that the number of elements of ( 20) is M n , indicating that the arbitrary n-degree N-variate orthogonal polynomial can be expressed using the linear combination of elements in (20). Thus,…”

Section: Orthogonal Polynomial Expansionmentioning

confidence: 99%

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Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility

Shiraya¹,

Yamakami²

2023

Preprint

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Copulas are used to construct joint distributions in many areas. In some problems, it is necessary to deal with correlation structures that are more complicated than the commonly known copulas. A finite order multivariate Hermite polynomial expansion, as an approximation of a joint density function, can handle complex correlation structures. However, it does not construct copulas because the density function can take negative values. In this study, we propose a method to construct a copula based on the finite sum of multivariate Hermite polynomial expansions by applying corrections to the joint density function.Furthermore, we apply this copula to estimate the volatility smile of cross currency pairs in the foreign exchange option market. This method can easily reproduce the volatility smile of cross currency pairs by appropriately adjusting the parameters and following the daily volatility fluctuations even if the higher-order parameters are fixed. In the numerical experiments, we compare the estimation results of the volatility smile of EUR-JPY with those of USD-JPY and EUR-USD for the proposed and other copulas, and show the validity of the proposed copula.

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Section: Orthogonal Polynomial Expansionmentioning

confidence: 99%

“…Therefore, many attempts have been made to apply copulas which can represent more complex correlation structures depending on problems. For example, Tavin [20] have proposed to use Bernstein polynomial copulas for multi-asset option pricing. Tavin [21] have applied copulas to measure dependence risk of a portfolio.…”

Section: Introductionmentioning

confidence: 99%

Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility

Shiraya¹,

Yamakami²

2023

Preprint

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“…Diers et al (2012) use Bernstein copulas to model the dependence between nonlife insurance risks. Tavin (2013) analyze properties of Bernstein copulas in a context of multiasset derivatives pricing. In contrast to Archimedean copulas, Bernstein copulas can model nonexchangeable dependence structures.…”

Section: Mixed Bernstein Copulasmentioning

confidence: 99%

Risk aggregation and capital allocation using a new generalized Archimedean copula

Marri¹,

Moutanabbir²

2021

Preprint

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In this paper, we address risk aggregation and capital allocation problems in the presence of dependence between risks. The dependence structure is defined by a mixed Bernstein copula which represents a generalization of the well-known Archimedean copulas. Using this new copula, the probability density function and the cumulative distribution function of the aggregate risk are obtained. Then, closed-form expressions for basic risk measures, such as tail value-atrisk (TVaR) and TVaR-based allocations, are derived.

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Second order risk aggregation with the Bernstein copula

Coqueret

2014

Insurance: Mathematics and Economics

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Application of Bernstein Copulas to the Pricing of Multi-Asset Derivatives

Cited by 4 publications

References 14 publications

Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility

Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility

Risk aggregation and capital allocation using a new generalized Archimedean copula

Second order risk aggregation with the Bernstein copula

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