Copula Methods in Finance

Cherubini, Umberto; Luciano, Elisa; Vecchiato, Walter

doi:10.1002/9781118673331

Cited by 1,328 publications

(922 citation statements)

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“…The copula models have been popular in the field of finance and insurance (e.g. Cherubini, 2004;Malevergne and Sornette, 2006;Kim and Lee, 2011;Choi et al ., 2013), and lately introduced in the fields of meteorology and hydrology (e.g., Favre et al ., 2004;Zhang and Singh, 2007;Genest and Favre, 2007). For a general discussion of copula, the readers are referred to Joe (1997) and Nelsen (2006).…”

Section: Introductionmentioning

confidence: 99%

Stochastic simulation of daily precipitation: A copula approach

Choi¹,

2014

Journal of the Korean Data and Information Science Society

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The traditional methods of simulating daily precipitation have paid little attention to the inherent dependence structure between the total precipitation amount and the precipitation frequency for a fixed period of time. To address this issue, we propose a new simulation algorithm using copula in order to incorporate the dependence into the traditional methods. The algorithm consists of two parts: First, while reflecting the observed dependence, we generate the total precipitation amount (S) and the frequency (N ) during the period of interest; then we simulate the daily precipitation whose aggregation matches the pair of (N, S) generated in the first part. Our result shows that the proposed method substantially improves the traditional methods.

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Section: Introductionmentioning

confidence: 99%

Stochastic simulation of daily precipitation: A copula approach

Choi¹,

2014

Journal of the Korean Data and Information Science Society

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“…This option pays one unit of currency if two stocks or indexes are above or below a pair of strike price levels. Options like these are very often used in structured finance, particularly index-linked products [2]. For example, assume the option of companies A and B has same exercise date T and strike prices K A and K B respectively, then the price of this digital put option[DP ] in a complete market is…”

Section: Digital Optionmentioning

confidence: 99%

“…While the tool is borrowed from the theory of statistics, it has been gathering more and more popularity both among academics and practitioners in the field of finance principally because of the intimate increase of volatility and erratic behavior of financial markets [2]. These new developments have caused standard tools of financial mathematics.…”

Section: Introductionmentioning

confidence: 99%

Digital Option Pricing Based on Copulas With Stochastic Simulation

Kim¹,

Kim²

2015

The Pure and Applied Mathematics

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Abstract. In this paper, we show the effectiveness of copulas by comparing the correlation of market data of year 2010 with those of years 2006-2009 and investigate copula functions as pricing methods of digital and rainbow options through real market data. We propose an accurate method of pricing rainbow options by using the correlation coefficients obtained from the copula functions depending on strike prices between assetes instead of simple traditional correlation coefficients.

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“…The empirical copula was correlating function. Generally, d-dimensional copula (C) can be presented (based on the Sklar theorem) (Cherubini et al, 2004) as a multidimensional distribution F, whose boundary functions (martingales) (F1, F2, ..., F d ) take the form of uniform distributions U(0,1) on the interval [0,1], which can be expressed in the form (2):…”

Section: The Technique Of Sampling Distributions and Correlating Varimentioning

confidence: 99%

The Impact of Variability of Selected Geological and Mining Parameters on the Value and Risks of Projects in the Hard Coal Mining Industry

Kopacz

2017

Archives of Mining Sciences

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The paper attempts to assess the impact of variability of selected geological (deposit) parameters on the value and risks of projects in the hard coal mining industry. The study was based on simulated discounted cash flow analysis, while the results were verified for three existing bituminous coal seams.The Monte Carlo simulation was based on nonparametric bootstrap method, while correlations between individual deposit parameters were replicated with use of an empirical copula. The calculations take into account the uncertainty towards the parameters of empirical distributions of the deposit variables. The Net Present Value (NPV) and the Internal Rate of Return (IRR) were selected as the main measures of value and risk, respectively.The impact of volatility and correlation of deposit parameters were analyzed in two aspects, by identifying the overall effect of the correlated variability of the parameters and the indywidual impact of the correlation on the NPV and IRR. For this purpose, a differential approach, allowing determining the value of the possible errors in calculation of these measures in numerical terms, has been used.Based on the study it can be concluded that the mean value of the overall effect of the variability does not exceed 11.8% of NPV and 2.4 percentage points of IRR. Neglecting the correlations results in overestimating the NPV and the IRR by up to 4.4%, and 0.4 percentage point respectively. It should be noted, however, that the differences in NPV and IRR values can vary significantly, while their interpretation depends on the likelihood of implementation.Generalizing the obtained results, based on the average values, the maximum value of the risk premium in the given calculation conditions of the "X" deposit, and the correspondingly large datasets (greater than 2500), should not be higher than 2.4 percentage points. The impact of the analyzed geological parameters on the NPV and IRR depends primarily on their co-existence, which can be measured by the strength of correlation. In the analyzed case, the correlations result in limiting the range of variation of the geological parameters and economics results (the empirical copula reduces the NPV and IRR in probabilistic approach). However, this is due to the adjustment of the calculation under conditions similar to those prevailing in the deposit. Keywords 546W publikacji podjęto próbę oceny wpływu zmienności wybranych parametrów geologicznych (złożowych) na wartość i ryzyko projektów w górnictwie węgla kamiennego. Badania przeprowadzono w ujęciu symulacyjnym z wykorzystaniem analizy zdyskontowanych przepływów pieniężnych oraz zweryfikowano na przykładzie trzech rzeczywistych pokładów węgla kamiennego.W symulacji Monte Carlo bazowano na technice bootstrapu nieparametrycznego, a zależności korelacyjne poszczególnych parametrów złożowych przestawiono przy pomocy kopuły empirycznej. W obliczeniach uwzględniono również niepewność wobec parametrów charakterystycznych rozkładów empirycznych zmiennych złożowych. Za wiodący miernik wartości wybrano...

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Copula Methods in Finance

Cited by 1,328 publications

References 0 publications

Stochastic simulation of daily precipitation: A copula approach

Stochastic simulation of daily precipitation: A copula approach

Digital Option Pricing Based on Copulas With Stochastic Simulation

The Impact of Variability of Selected Geological and Mining Parameters on the Value and Risks of Projects in the Hard Coal Mining Industry

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