Informatics Publishing Limited

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

Affiliations
1 KL University, Vaddeswaram, Guntur District - 522502, Andhra Pradesh, IN
2 JNTU Kakinada, Kakinada - 533003, Andhra Pradesh, IN

Abstract

Background/Objectives: The main objective of this paper is to present an n-step binomial model which can be used to price an option under any exotic conditions. Methods/Statistical Analysis: Mathematical models have been presented using which an n-step binomial model can be developed. The model can be used for estimating price of options under n of number exotic conditions that influence the option price. Findings: Pricing of exotic options like Asian, American etc., undertaken through Binomial Trees using only one-step considering maximum and minimum values that can be taken by the underling at the maturity leads to a rough approximation of the option price. The approximation is possible by assuming stock price movements to be in one or two binomial steps during the life of the option. A binomial tree extended to an N-step Model can be used to price various exotic options. A study of the convergence in European option price with respect to Number of steps (N) and variation in price of Asian and American options with respect to confidence factor (k) (proxy for implied volatility) using the maximum and minimum boundaries on the value of k gives the investors the ability to change the value of k so that they can have their own opinions concerning the risk-neutral probability distribution.

Keywords

Binomial Tree, Implied Volatility, Pricing Options.

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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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