Research Article Open Access

Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas

Jimbo Henri Claver1, Tatanfack Emerson2 and Shu Felix2
  • 1 Department of Mathematics and Computing, American International University, Kuwait
  • 2 Department of Mathematics and Computer Science, University of Bamenda, Cameroon

Abstract

Recently, it has been reported that the hypothesis proposed by the classical black scholes model to price multivariate options in finance were unrealistic, as such, several other methods have been introduced over the last decades including the copulas methods which uses copulas functions to model the dependence structure of underlying assets. However, the previous work did not take into account the use of mixed copulas to assess the underlying assets' dependence structure. The approach we propose consists of selecting the appropriate mixed copula’s structure which captures as much information as possible about the asset’s dependence structure and apply a copulas-based martingale strategy to price multivariate equity options using monte Carlo simulation. A mixture of normal distributions estimated with the standard EM algorithm is also considered for modeling the marginal distribution of financial asset returns. Moreover, the Monte Carlo simulation is performed to compute the values of exotic and up and out barrier options such as worst of, spread, and rainbow options, which shows that the clayton gumble and clayton gaussian have relatively large values for all the options. Our results further indicate that the mixed copula-based approach can be used efficiently to capture heterogeneous dependence structure existing in multivariate assets, price exotic options and generalize the existing results.

Journal of Mathematics and Statistics
Volume 19 No. 1, 2023, 1-12

DOI: https://doi.org/10.3844/jmssp.2023.1.12

Submitted On: 19 September 2022 Published On: 3 April 2023

How to Cite: Claver, J. H., Emerson, T. & Felix, S. (2023). Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas. Journal of Mathematics and Statistics, 19(1), 1-12. https://doi.org/10.3844/jmssp.2023.1.12

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Keywords

  • Monte Carlo Simulation
  • Dependence Structure
  • Exotic and Barrier Options
  • Copulas Method
  • Gaussian Mixture Distributions
  • and Mixted Copulas
  • Black Scholes Model