Multivariate Option Pricing with Gaussian Mixture Distributions and Mixed Copulas

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