Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas
- 1 Department of Mathematics and Computing, American International University, Kuwait
- 2 Department of Mathematics and Computer Science, University of Bamenda, Cameroon
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.
Copyright: © 2023 Jimbo Henri Claver, Tatanfack Emerson and Shu Felix. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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- Monte Carlo Simulation
- Dependence Structure
- Exotic and Barrier Options
- Copulas Method
- Gaussian Mixture Distributions
- and Mixted Copulas
- Black Scholes Model