scholarly journals Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abba Mallam Hassane ◽  
Barro Diakarya ◽  
Yaméogo WendKouni ◽  
Saley Bisso
Keyword(s):  
Extreme Values ◽  
Asset Returns ◽  
Copula Function ◽  
Dependence Structure ◽  
Mixture Distributions ◽  
Equity Options ◽  
Financial Asset Returns ◽  
Equity Option ◽  
Digital Option ◽  
European Equity

In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

scholarly journals Calibrating and Simulating Copula Functions in Financial Applications

2021 ◽  
Vol 7 ◽  
Author(s):  
Annalisa Di Clemente ◽  
Claudio Romano
Keyword(s):  
Financial Market ◽  
Asset Returns ◽  
Copula Function ◽  
Dependence Structure ◽  
Financial Asset ◽  
Financial Assets ◽  
Copula Functions ◽  
Financial Applications ◽  
Different Types ◽  
Financial Asset Returns

Copula functions can be utilized in financial applications to determine the dependence structure of the financial asset returns in the portfolio. Empirical evidence has proved the inadequacy of the multi-normal distribution, traditionally adopted to model the financial asset returns distribution. Copula functions can be employed in a flexible way for building efficient algorithms and to simulate a more adequate distribution of the financial assets. This paper aims to describe some simple statistical procedures currently employed to calibrate the copula functions to the financial market data. Furthermore, we present some useful methods for choosing which copula function better fits the real financial data. Also, some algorithms to simulate random variates from certain types of copula functions are illustrated. Finally, for illustration purposes, the previous procedures described are applied to two Italian equities. In particular, we show how to generate efficient Monte Carlo scenarios of equity log-returns in the bivariate case using different types of copula functions.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

scholarly journals Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Nachatchapong Kaewsompong ◽  
Paravee Maneejuk ◽  
Woraphon Yamaka
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Method ◽  
Real Data ◽  
Copula Function ◽  
Dependence Structure ◽  
Simulation Studies ◽  
Multivariate Normal ◽  
Empirical Comparison ◽  
Proposed Model ◽  
Conventional Models

We propose a high-dimensional copula to model the dependence structure of the seemingly unrelated quantile regression. As the conventional model faces with the strong assumption of the multivariate normal distribution and the linear dependence structure, thus, we apply the multivariate exchangeable copula function to relax this assumption. As there are many parameters to be estimated, we consider the Bayesian Markov chain Monte Carlo approach to estimate the parameter interests in the model. Four simulation studies are conducted to assess the performance of our proposed model and Bayesian estimation. Satisfactory results from simulation studies are obtained suggesting the good performance and reliability of the Bayesian method used in our proposed model. The real data analysis is also provided, and the empirical comparison indicates our proposed model outperforms the conventional models in all considered quantile levels.

scholarly journals ESTIMASI NILAI CONDITIONAL VALUE AT RISK MENGGUNAKAN FUNGSI GAUSSIAN COPULA

2015 ◽  
Vol 4 (4) ◽  
pp. 188
Author(s):  
HERLINA HIDAYATI ◽  
KOMANG DHARMAWAN ◽  
I WAYAN SUMARJAYA
Keyword(s):  
At Risk ◽  
Confidence Level ◽  
Value At Risk ◽  
Risk Measure ◽  
Copula Function ◽  
Gaussian Copula ◽  
Nonlinear Dependence ◽  
Conditional Value At Risk ◽  
Dependence Structure ◽  
Measurement Tools

Copula is already widely used in financial assets, especially in risk management. It is due to the ability of copula, to capture the nonlinear dependence structure on multivariate assets. In addition, using copula function doesn’t require the assumption of normal distribution. There fore it is suitable to be applied to financial data. To manage a risk the necessary measurement tools can help mitigate the risks. One measure that can be used to measure risk is Value at Risk (VaR). Although VaR is very popular, it has several weaknesses. To overcome the weakness in VaR, an alternative risk measure called CVaR can be used. The porpose of this study is to estimate CVaR using Gaussian copula. The data we used are the closing price of Facebook and Twitter stocks. The results from the calculation using 90%  confidence level showed that the risk that may be experienced is at 4,7%, for 95% confidence level it is at 6,1%, and for 99% confidence level it is at 10,6%.

scholarly journals A Copula Entropy Approach to Dependence Measurement for Multiple Degradation Processes

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 724 ◽  
Author(s):  
Fuqiang Sun ◽  
Wendi Zhang ◽  
Ning Wang ◽  
Wei Zhang
Keyword(s):  
Information Entropy ◽  
Complex Structure ◽  
Copula Function ◽  
Dependence Structure ◽  
Entropy Theory ◽  
Multiple Features ◽  
Reliability Modeling ◽  
Degradation Processes ◽  
Degradation Analysis ◽  
Complex Dependence

Degradation analysis has been widely used in reliability modeling problems of complex systems. A system with complex structure and various functions may have multiple degradation features, and any of them may be a cause of product failure. Typically, these features are not independent of each other, and the dependence of multiple degradation processes in a system cannot be ignored. Therefore, the premise of multivariate degradation modeling is to capture and measure the dependence among multiple features. To address this problem, this paper adopts copula entropy, which is a combination of the copula function and information entropy theory, to measure the dependence among different degradation processes. The copula function was employed to identify the complex dependence structure of performance features, and information entropy theory was used to quantify the degree of dependence. An engineering case was utilized to illustrate the effectiveness of the proposed method. The results show that this method is valid for the dependence measurement of multiple degradation processes.

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