This study examines the efficiency of the overall Indian banking industry using Data Envelopment Analysis (DEA) and to perform a comparative efficiency analysis of public, private, and foreign banks using six varied forms. Also, providing ranks to the banks based on their efficiency. The study incorporates BCC output-oriented DEA model using a sample of 50 Indian banks (public banks = 17, private banks = 18, foreign banks = 15) for a period ranging from 2009-10 to 2018-19, hence incorporating the after-effects of the financial crisis and demonetization, this study uses panel data from 2009-10 to 2018-19. The results showed that most of the Indian banks fall on the efficient side or are near to full efficiency. However, public banks outperform private and foreign banks in terms of their average efficiency. Results also specify that the performance of banks is sensitive to input-output variables, units under evaluation, and choice of the model. The current study has just focused on the internal factors for analyzing the efficiency of Indian banks; however, certain external factors might also impact the banks’ efficiency.

Asset Liability Management has gained popularity in the banking sector. Earlier banks focused on asset allocation, but now the management of assets and liabilities is equally essential. Asset liability management targets the optimum distribution of funds in assets and managing liabilities so that banks can earn higher profits and minimize risk. In this paper, the optimization of assets and liabilities of Indian banks has been concentrated using mathematical models. Combining the Analytical Hierarchy Process (AHP) and Goal Programming (GP) model has been used to solve the optimization problem. AHP is a multi-criteria decision-making approach for deriving priority weights. Goal Programming is a linear programming model to solve complex issues having multiple objectives. In this paper, the primary data gathered from Bank senior managers have been analyzed using the AHP approach to derive weights for criteria. These weights are assigned to goals in goal programming to prioritize the goals. Secondary data on OBC bank is used in goal programming from 2010-2019 collected from OBC bank's annual reports and RBI websites. The findings show that OBC bank has the scope of improving its assets and liabilities position to increase its profit and minimize the risk. The model generates an optimum balance sheet that achieves the set goals and satisfies all the statutory and planning constraints. The same model can be useful for scheduled commercial banks in India with modifications concerning banks' targets and controls. The model developed in this paper is helpful for bank managers in planning and forecasting. AHP and GP's combined approach is unique in this paper, which uses experts' knowledge and applies it in the model. The model is created on the bank's realistic goals and constraints after carefully considering the issues faced by bank officials. The paper is limited to the Indian Banking system as other countries have different balance sheet structures and constraints.

In earlier years, there was abundance of funds in banks in the form of demand and savings deposits. Hence, the focus of banks was mainly on asset management. But intense competition and volatility of interest rate due to banking reforms reduced the availability of low-cost funds and therefore, banks focused on liability management as well. These pressures call for structured and comprehensive measures and not just ad hoc action. This is how banks started to concentrate more on the management of both sides of the balance sheet. As a result, the concept of asset-liability management originated in India and introduced in the Indian banking industry since 1st April 1999 to administer the risk management aspects. This paper attempts to optimize assets and liabilities of banks using goal programming technique. Secondary data is collected from annual reports of Allahabad bank from 2010-2019 and RBI website is used for modelling. The findings show that in Allahabad bank, goal programming help in achieving optimization and increase profitability. The model incorporating constraints and set objectives. It model can support banks in decision making process, planning, budgeting, and forecasting. An attempt is made to use realistic goals and constraints after discussing with bank officials. JEL Classification Codes: C61, G21, G32.

Options are used by hedgers to reduce risk. A better way implemented by the companies these days is to use the delta value of options to create a portfolio having minimum risk. This portfolio has a delta value of zero. Due to the market changes the delta value changes and thus the portfolio needs to be balanced regularly. In this study, it was observed the delta value of six options of March expiry and six options of April expiry of Nifty which is traded over National Stock Exchange over the time period of 4th March to 15th April, 2010. With the help of delta values, a portfolio has been created using a call and put option of strike price Fifty One Hundred. The changes in the market over this period have been reflected in the delta values and accordingly the portfolio has been rebalanced on a per day basis. Along with this, various hypothesis regarding options have been tested. The different types of options have been analyzed and the most expensive and cheapest ones have been identified. The relation between time value of option and time of maturity has been verified. The volatility of options has been compared with market volatility and also with the strike price of respective option. These findings are explained theoretically and finally tested on the touchstone of historical data collected from the site of National Stock Exchange and values calculated with the help of standard formulae already available. The findings of the study are in consonance with the various theories about Options available. On the basis of the study conducted in furtherance of this project the author concludes that in the time period assumed, the delta neutral portfolio created was profitable for option expiring in April while was in loss for March expiry.

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