Informatics Publishing Limited

D. Kavitha ¹, V. Kamakshi Prasad ², J. V. R. Murthy ³

Affiliations
1 PVPSIT, Vijayawada - 520007, Andhra Pradesh, IN
2 Department of Computer Science and Engineering, JNTUH College of Engineering, JNTU Hyderabad - 500085, Telangana, IN
3 Department of Computer Science and Engineering, JNTU Kakinada, Kakinada – 533003, Andhra Pradesh, IN

Abstract

Objectives: To mine significant subgraphs with user specified objective functions from a set of graphs that are useful for understanding the intrinsic characteristics of data in a scalable approach. Methods/Statistical Analysis: A large number of candidate subgraphs generated during mining process causes both computational and statistical problem. In this paper, Significant SubGraph Mining-SSGM proposes an algorithm to find significant subgraphs by using a small set of representative patterns - coreset that overcomes these problems. Furthermore, an edge graph notation is used to represent a graph that enables to mine patterns directly without using separate mining algorithm. Findings: The number of possible candidates is generally exponential in search space and techniques employed are mostly focussed on monotonic property. The proposed algorithm offers simple, yet efficient optimizations to significantly improve performance by pruning the search space and exploring representative graphs. It avoids enumeration of all frequent subgraphs which cause redundancy and extreme mining time. The identified coreset elements are extended that provide optimal solution patterns and adopted edge graph notation mine subgraphs directly. Application/Improvements: Experimental results shows that the proposed algorithm is effective and efficient for mining significant subgraphs in terms of computational cost, scalability and time over existing methods. The algorithm can be applied to find different types of significant patterns in a scalable manner by using any objective function according to the problem domain including support, correlation measure and feature set.

Keywords

Frequent Graphs, Objective Function, Representative Set, Statistical Significance, Subgraph Mining.

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Sastry K. R. Jammalamadaka ¹, K. V. N. M. Ramesh ², J. V. R. Murthy ²

Affiliations
1 Department of Electronics and Computer Engineering, KL University, Vaddeswaram - 522502, Andhra Pradesh, IN
2 Jawaharlal Nehru Technological University, Kakinada – 533003, Andhra Pradesh, IN

Abstract

Measurement of market risk requires lots of computational resources when the Value-at-Risk (VaR) is computed using the historical simulation approach as it involves full revaluation of the portfolio for the considered data points. Although approximations can be done using the delta-normal, delta-gamma and delta-gamma-theta approaches, historical simulation approach alone is straight forward method that uses past data to generate future values without assuming any distribution for the underlying returns. The requirement of intensive computational effort in case of historical simulation hinders it’s usage for applying to real time VaR calculation. In this work we propose a methodology that doesn’t forego the benefits of historical simulation approach but can be applied to calculate market risk VaR in real time. The VaR calculated using the proposed methodology converges as the range of the portfolio returns is increased. The proposed methodology is also superior to the historical simulation approach in terms of usage of the computational resources and applicability to real time without sacrificing accuracy obtained using historical simulation approach.

Keywords

Portfolio Assessment, Risk Assessment, Risk Assessment through Simulation, Share Market, Value-at-Risk.

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Sastry K. R. Jammalamadaka ¹, K. V. N. M. Ramesh ², J. V. R. Murthy ²

Affiliations
1 Department of Electronics and Computer Engineering, KL University, Vaddeswaram, Guntur – 522502, Andhra Pradesh, IN
2 Jawaharlal Nehru Technological University, Kakinada - 533003, Andhra Pradesh, IN

Abstract

Background/Objectives: The main objective of this paper is to compute VaR (Value at risk) which requires minimal resources and the computing is done in real-time with utmost accuracy. Method/Statistical Analysis: The paper presents a methodology which helps in computing VaR in real time and with most accuracy. Very less computational resources are required from computing VaR. The VaR computing methodology proposed in this paper converges as the returns on the portfolio ranges increases. Findings: It has been presented in the paper that the number of valuations required for computing the VaR is dependent on the number of instruments added to the portfolio and is independent of the number of instruments already existing at the time computing VaR. The method proposed in this paper can be used for computing VaR in real time.

Keywords

Market Risk, Portfolio Instruments, Risk Assessment, Real-Time Market Risk Measurement, VaR

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Sastry K. R. Jammalamadaka ¹, K. V. N. M. Ramesh ², J. V. R. Murthy ²

Affiliations
1 Department of Electronics and Computer Engineering, Computer Science and Engineering, KL University, Vaddeswaram, Guntur District - 522502, Andhra Pradesh, IN
2 Jawaharlal Nehru Technological University, Kakinada - 533503, Andhra Pradesh, IN

Abstract

Background/Objectives: The main objective of this paper is to present a method that determines optimum collateral amount at which the risk of the venerable option is same as the exchange traded risk. Methods/Statistical Analysis: Mathematical models have been presented in this paper that is related to binomial tree building, Venerable option pricing. An algorithm has also been presented to calculate minimum collateral amount. Experimental models demonstrate the Convergence of Collateral amount and Sensitivity of Vulnerable Option Price to Model Parameters, and Correctness of the optimum collateral amount. Findings: A methodology has been presented in this paper that can be used to compute maximum collateral amount that must be supported by the writer of the option at which the venerable option becomes as risky as the exchange traded risk. This methodology can also be sued when the option writers chooses a fixed collateral amount when the underlying price is greater than the fixed price. A navel binomial decision has been developed and presented considering no assumption of the underlying distribution. It has been found that the price of an option with credit risk converges to exchange traded option as the collateral amount reaches a certain optimal value. The option writer in this can case can use the excess collateral amount for some other purpose. It has also been found that rules that are related to plain vanilla option need not be followed for calculating venerable option.

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J. K. R. Sastry ¹, K. V. N. M. Ramesh ², J. V. R. Murthy ²

Affiliations
1 KL University, Vaddeswaram, Guntur District - 522502, Andhra Pradesh, IN
2 Jawaharlal Nehru Technological University, Kakinada - 533503, Andhra Pradesh, IN

Abstract

Background/Objectives: The main objective of this paper is to present a model that takes bankruptcy of the seller while calculating the risk involved in fixing the premium at which the underlying options are sold. Methods/Statistical Analysis: A mathematical model which is based on probability distribution have been presented in the paper that extends the binary decision tree model to include bankruptcy for assessing the risk in selling underlying option at premium. Findings: A novel method has been presented that extends the binomial tree for taking into account default probability of the seller. The model can be used by the option seller for computing the risks involved in fixing the premium at which the options can be sold. It has been observed that the option prices considering the bankruptcy are higher compared to the option prices without bankruptcy.

Keywords

Bankruptcy, Pricing Option, Underlying Issuer

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D. J. Nagendra Kumar , J. V. R. Murthy

Abstract

Expectation Maximization (EM) is an efficient mixture-model based clustering method. In this paper, authors made an attempt to scale-up the algorithm, by reducing the computation time required for computing quadratic term, without sacrificing the accuracy. Probability density function (pdf) is to be calculated in EM, which involves evaluating quadratic term calculation. Three recursive approaches are introduced for quadratic term computation. As per our observation, the standard EM needs O(d² ) computations for quadratic term computation, where d is number of dimensions. The proposed recursive EM approaches are with time complexity of O(d²/2) for the quadratic term computation.

Keywords

Expectation Maximization, Quadratic Term, Speed-up-Lower, Triangular, Canonical Form-Forward Substitution.

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