scholarly journals Multivariate Option Pricing with Pair-Copulas

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Anna Barban ◽  
Luca Di Persio
Keyword(s):  
Option Pricing ◽  
Decomposition Method ◽  
General Procedure ◽  
Composite Index ◽  
Simulated Data ◽  
Dependence Structure ◽  
Main Difficulty ◽  
Comparison Analysis ◽  
Nasdaq Composite Index ◽  
Proposed Model

We propose a copula-based approach to solve the option pricing problem in the risk-neutral setting and with respect to a structured derivative written on several underlying assets. Our analysis generalizes similar results already present in the literature but limited to the trivariate case. The main difficulty of such a generalization consists in selecting the appropriate vine structure which turns to be of D-vine type, contrary to what happens in the trivariate setting where the canonical vine is sufficient. We first define the general procedure for multivariate options and then we will give a concrete example for the case of an option written on four indexes of stocks, namely, the S&P 500 Index, the Nasdaq 100 Index, the Nasdaq Composite Index, and the Nyse Composite Index. Moreover, we calibrate the proposed model, also providing a comparison analysis between real prices and simulated data to show the goodness of obtained estimates. We underline that our pair-copula decomposition method produces excellent numerical results, without restrictive assumptions on the assets dynamics or on their dependence structure, so that our copula-based approach can be used to model heterogeneous dependence structure existing between market assets of interest in a rigorous and effective way.

Messages of Oscillatory Correlograms: A Spike Train Model

2008 ◽  
Vol 20 (5) ◽  
pp. 1211-1238 ◽  
Author(s):  
Gaby Schneider
Keyword(s):  
Spike Train ◽  
Null Model ◽  
Simulated Data ◽  
Joint Analysis ◽  
Data Set ◽  
Proposed Model ◽  
Peak Asymmetry ◽  
Millisecond Range ◽  
Temporal Interactions ◽  
Underlying Processes

Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry. The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.

On the Rapid Generation of Complete XRF Spectra for Material Analysis from Fundamental Parameters

2021 ◽  
Vol 105 ◽  
pp. 110-118
Author(s):  
Jie Si Ma ◽  
Fu Sheng Li ◽  
Yan Chun Zhao
Keyword(s):  
Simulated Data ◽  
Target Material ◽  
Mcnp Code ◽  
X Ray ◽  
Fundamental Parameters ◽  
Elemental Compositions ◽  
Statistical Precision ◽  
Proposed Model ◽  
Time Calculation ◽  
Rapid Generation

X-ray Fluorescence (XRF) analysis technology is used widely to detect and measure elemental compositions of target samples. The MCNP code developed by LANL can be utilized to simulate and generate the XRF spectrum of any sample with various elemental compositions. However, one shortcoming of MCNP code is that it takes quite a lot of time (in hours or longer) to generate one XRF spectrum with reasonable statistical precision; the other shortcoming is that MCNP code cannot produce L shell spectrum accurately. In this paper, a new computation model based on the Sherman equation (i.e., Fundamental Parameters, FP) is proposed to overcome the drawbacks of the MCNP code. The most important feature of this model is to achieve a full and accurate generation of spectral information of each element in a target material very rapidly (in seconds or less), including both K and L shell spectral peaks. Furtherly, it is demonstrated that the simulated data by this new mode match the experimental data very well. It proves that the proposed model can be a better alternative of MCNP code in the application of generation the XRF spectra of many materials, in terms of speed and accuracy. The proposed model can perform the simulation of XRF spectra in situ both fast and accurately, which is essential for real-time calculation of chemical composition by use of X-ray spectrometer, especially for those trace elements in target materials.

scholarly journals The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 780-785 ◽  
Author(s):  
Sunday O. Edeki ◽  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Grace O. Akinlabi
Keyword(s):  
Analytical Solution ◽  
Option Pricing ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Asian Option ◽  
Pricing Model ◽  
Adomian Decomposition ◽  
Option Pricing Model ◽  
Option Model ◽  
High Level

Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

scholarly journals Regime-Switching Behaviour In US Equity Indices: Two State Model With Kalman Filter Tracking And Finite State Machine Trading System

2021 ◽  
Author(s):  
Timothy Little
Keyword(s):  
Regime Switching ◽  
Finite State Machine ◽  
Composite Index ◽  
State Machine ◽  
Trading System ◽  
Switching Model ◽  
Nasdaq Composite Index ◽  
Finite State ◽  
Equity Index ◽  
Equity Indices

This thesis presents a time varying regime-switching model for US equity index daily returns. The parameters of the model are estimated recursively with the Kalman lter. We demonstrate our model and parameter estimation technique are effective by demonstrating improvements in model t compared to alternate models. Information from our model is used to build a Finite State Machine trading system with back-tested performance in excess of 15,000% above a buy and hold strategy for the DOW Jones Industrial average from 1928-2012. Similar results are found for both the S&P 500 index and the NASDAQ Composite index over a long period. Our model succeeds at identifying pro table investment opportunities and improving model t with a minimum of parameters.

scholarly journals Streamflow estimation at partially gaged sites using multiple dependence conditions via vine copulas

2020 ◽  
Author(s):  
Kuk-Hyun Ahn
Keyword(s):  
Missing Values ◽  
The Other ◽  
Dependence Structure ◽  
Proposed Model ◽  
Pee Dee ◽  
Streamflow Estimation ◽  
Vine Copula ◽  
Bivariate Copula ◽  
Pee Dee River ◽  
Vine Copulas

Abstract. Reliable estimates of missing streamflow values are relevant for water resources planning and management. This study proposes a multiple dependence condition model via vine copulas for the purpose of estimating streamflow at partially gaged sites. The proposed model is attractive in modeling the high dimensional joint distribution by building a hierarchy of conditional bivariate copulas when provided a complex streamflow gage network. The usefulness of the proposed model is firstly highlighted using a synthetic streamflow scenario. In this analysis, the bivariate copula model and a variant of the vine copulas are also employed to show the ability of the multiple dependence structure adopted in the proposed model. Furthermore, the evaluations are extended to a case study of 54 gages located within the Yadkin-Pee Dee River Basin, the eastern U. S. Both results inform that the proposed model is better suited for infilling missing values. After that, the performance of the vine copula is compared with six other infilling approaches to confirm its applicability. Results demonstrate that the proposed model produces more reliable streamflow estimates than the other approaches. In particular, when applied to partially gaged sites with sufficient available data, the proposed model clearly outperforms the other models. Even though the model is illustrated by a specific case, it can be extended to other regions with diverse hydro-climatological variables for the objective of infilling.

scholarly journals Dependence structure analysis of multisite river inflow data using vine copula-CEEMDAN based hybrid model

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10285
Author(s):  
Hafiza Mamona Nazir ◽  
Ijaz Hussain ◽  
Muhammad Faisal ◽  
Alaa Mohamd Shoukry ◽  
Mohammed Abdel Wahab Sharkawy ◽  
...  
Keyword(s):  
River Basin ◽  
Hybrid Model ◽  
Moving Average ◽  
Ensemble Empirical Mode Decomposition ◽  
Dependence Structure ◽  
Absolute Deviation ◽  
River Inflow ◽  
Multi Scale ◽  
Proposed Model ◽  
Vine Copula

Several data-driven and hybrid models are univariate and not considered the dependance structure of multivariate random variables, especially the multi-site river inflow data, which requires the joint distribution of the same river basin system. In this paper, we proposed a Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) Vine copula-based approach to address this issue. The proposed hybrid model comprised on two stages: In the first stage, the CEEMDAN is used to extract the high dimensional multi-scale features. Further, the multiple models are used to predict multi-scale components and residuals. In the second stage, the residuals obtained from the first stage are used to model the joint uncertainty of multi-site river inflow data by using Canonical Vine. For the application of the proposed two-step architecture, daily river inflow data of the Indus River Basin is used. The proposed two-stage methodology is compared with only the first stage proposed model, Vector Autoregressive and copula-based Autoregressive Integrated Moving Average models. The four evaluation measures, that is, Mean Absolute Relative Error (MARE), Mean Absolute Deviation (MAD), Nash-Sutcliffe Efficiency (NSE) and Mean Square Error (MSE), are used to observe the prediction performance. The results demonstrated that the proposed model outperforms significantly with minimum MARE, MAD, NSE, and MSE for two case studies having significant joint dependance. Therefore, it is concluded that the prediction can be improved by appropriately modeling the dependance structure of the multi-site river inflow data.

scholarly journals Use of Correlated Data for Nonparametric Prediction of a Spatial Target Variable

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2077
Author(s):  
Pilar García-Soidán ◽  
Tomás R. Cotos-Yáñez
Keyword(s):  
Spatial Data ◽  
Lead Level ◽  
Simulated Data ◽  
Auxiliary Variable ◽  
Correlated Data ◽  
Dependence Structure ◽  
Nonparametric Approach ◽  
Additional Information ◽  
Squared Prediction Error ◽  
Kernel Approach

The kriging methodology can be applied to predict the value of a spatial variable at an unsampled location, from the available spatial data. Furthermore, additional information from secondary variables, correlated with the target one, can be included in the resulting predictor by using the cokriging techniques. The latter procedures require a previous specification of the multivariate dependence structure, difficult to characterize in practice in an appropriate way. To simplify this task, the current work introduces a nonparametric kernel approach for prediction, which satisfies good properties, such as asymptotic unbiasedness or the convergence to zero of the mean squared prediction error. The selection of the bandwidth parameters involved is also addressed, as well as the estimation of the remaining unknown terms in the kernel predictor. The performance of the new methodology is illustrated through numerical studies with simulated data, carried out in different scenarios. In addition, the proposed nonparametric approach is applied to predict the concentrations of a pollutant that represents a risk to human health, the cadmium, in the floodplain of the Meuse river (Netherlands), by incorporating the lead level as an auxiliary variable.

scholarly journals Fractional Order Stochastic Differential Equation with Application in European Option Pricing

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Qing Li ◽  
Yanli Zhou ◽  
Xinquan Zhao ◽  
Xiangyu Ge
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Option Pricing ◽  
Memory Effect ◽  
Fractional Order ◽  
Mean Value ◽  
European Option ◽  
European Option Pricing ◽  
Proposed Model ◽  
Pricing Formula

Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.

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.

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