Project Trainee : Abhinav Yellanki 5 th year Integrated M.Sc. Student Mathematics and Computing Indian Institute of Technology, Kharagpur

Transcription

1 SIMULATION MODELLING OF ASSETS AND LIABILITI ES OF A BANK Project Trainee : Abhinav Yellanki 5 th year Integrated M.Sc. Student Mathematics and Computing Indian Institute of Technology, Kharagpur Project Guide : Dr V.N. Sastry Professor IDRBT, Hyderabad Date : 9 th July,

2 CERTIFICATION This is to certify that project report titled SIMULATION MODELLING OF ASSETS AND LIABILITIES OF BANK submitted by Mr. Abhinav Yellanki of 5th year, Integrated M.Sc., Maths and Computing, IIT Kharagpur is a record of a bonafide work carried out by him under my guidance during the period 9th may, 2012 to 9th July, 2012 at Institute for Development and Research in Banking Technology, Hyderabad. Dr. V. N. Sastry (Project Guide) Professor IDRBT, Hyderabad 2

3 ACKNOWLEDGEMENT I declare that the summer internship project report titled SIMULATION MODELLING OF ASSETS AND LIABILITIES OF A BANK is my own work carried under the supervision of Prof V.N. Sastry at the Institute for Development and Research in Banking Technology, Hyderabad in the period from 9 th May, 2012 to 9 th July, I further declare that to the best of my knowledge, the report does not contain any part of any work which has been submitted for the award of any degree either in this institute or any other institute without proper citation. Abhinav Yellanki 5 th year Integrated M.Sc. Student Mathematics and Computing IIT, KHARAGPUR. 3

4 ABSTRACT Banking has a long and honourable history. Today it encompasses a wide range of activities, of varying degrees of complexity. The common denominators for all banking activities are those of risk, return and bringing together of the providers of capital. The coordination of all banking activities is the main focus of asset liability and management (ALM) desk. ALM of a bank performs risk analysis for different risks. Simulation modelling is one of the models used to perform this analysis. Simulation allows more dynamic evaluation of risk. Advances in technology and the development and refinement of asset-liability software have made earnings simulation models an increasingly practical tool for asset liability management and control. Here in this report we try to demonstrate building of one such tool which can perform ALM analysis regularly day by day. 4

5 INDEX 1. Introduction 1.1. Asset Liability and Management (ALM) 1.2. RBI Guidelines 1.3. Organisation of project work 2. Simulation Modelling 2.1. Monte-Carlo simulation 2.2. Random Number generators (RNGs) 2.3. Tests for RNGs 3. Design of Algorithm 3.1. For Branch level Simulation and ALM 3.2. For Bank level Simulation and ALM 4. Observations and Conclusion References 5

6 1. INTRODUCTION 1.1. Asset-liability management (ALM) Asset-liability management is a generic term used to refer a number of things by different market participants. However it denotes the high level management of bank s assets (ALCO). The principle function in ALM is to increase the value of the bank s capital and assets. This in short means management of Liquidity risk and Interest rate risk. It will also set the overall policy for credit risk and credit risk management. An ALM trading desk must manage these Assets and liabilities for Interest rate risk and liquidity risk and increase the returns of the bank. ASSETS OF BANK: Cash, Investments, loans & advances, Balance with RBI and other Banks, Fixed Assets, NPA s, Assets on lease and other Assets. LIABILITIES OF BANK Term deposits, demand deposits, Borrowings, Bonds, Capitals, Reserves & Surplus, Other Liabilities. These assets and liabilities are classified into different term buckets based on their maturity dates. The mismatch between different terms of assets and liabilities across term structure is called liquidity gap. The mismatch between different interest rates that each asset or liability contract struck at is called interest rate gap. Liquidity risk exposure arises from normal banking operations. That is, it exists irrespective of the type of funding gap a, be it excess assets over liabilities for any particular time bucket or an excess of liabilities over assets. There is a funding risk in any case, either fund must be obtained or surplus assets are laid off. Liquidity risk in itself generates Interest-rate risk, due to uncertainty of future interest rates. This can be managed through hedging. If assets are of floating rate, there is less concern over interest rate risk because of the nature of interest rate reset. This also applies to floating-rate liabilities, but only insofar that these match floating rate assets. Even if both 6

7 assets and liabilities are floating rate, they can still generate interest-rate risk due to difference in payment periods of Libor for assets and liabilities. Liquidity risk can be managed by matching assets and liabilities, or by setting a series of rolling term loans to fund long dated assets. Generally banks will have a particular view of future market conditions, and manage the ALM book in line with this view Reserve Bank of India (RBI) Guidelines The assets and liabilities are divided into buckets and managed accordingly. RBI made few norms to control the mismatches (outflows- inflows) between assets and liabilities in the maturity buckets of a bank. Norms on the cumulative negative mismatches are as follows (next day) - 5% (2-7days) - 10% (8-14days) - 15% (15-28days) - 20% 1.3. Organization of project work Objective: Design a prototype, which can simulate the data of assets and liabilities for a branch by taking two parameters amount and maturity. These generated deposits and liabilities are kept into respective maturity buckets and are verified for RBI norms, if these norms are not met bucket structure is reconstructed by disinvesting and investing. Then this reconstructed bucket structure is analyzed for profit optimization in different scenarios with respect to interest rate variation. Achievement: Designed the above mentioned prototype. For this we are using simulation modelling approach. For simulation of data we are using Monte- Carlo simulation by taking amount and maturity period as parameters. We have implemented this design using Matlab. 7

8 2. SIMULATION MODELLING Simulation modelling [2] is a procedure that measures the potential impact on the banking book, for a user specified change in interest rate or change in shape of book itself. This procedure enables the senior management to gauge risk associated with the strategies in different scenarios. It is an iterative process in which the simulation model produces complete earning results for each specific set of values for the chosen scenarios. The process lets the banker observe a pattern of earning implied in the present and planned balance sheet under alternative forecast of future yield curves. Depending on the software capability earning simulation can be increased to any level of sophistication desired. Figure (i): approach to simulation in its simplest for is depicted below: DATA ASSUMPTION Current business Composition of 1) Balance sheet. 2) Interest Rates. 3) Malurities. 4) Repricing. 1) Rates. 2) Business mix. 3) Growth. 4) New. 5) Products. What if Analysis OUTPUT Decision The basic requirements for simulation modelling are large volume of data, projection of volume, mix, etc. of business and rapid processing computer and 8

9 efficient manpower to evaluate the Simulation results. Bank balance sheets change dramatically with changing interest rates. The rapidity with which the banks can restructure their balance sheet is indication of the type knowledgeable data input that would be required to apply simulation technique. To simulate the assets and liabilities we use the Monte-Carlo simulation by taking amount deposited/loaned and maturity period of deposit/loan as parameters Monte-Carlo Simulation: Monte-Carlo is the code name given by Von Newmann and S.M.Ulam to the technique of solving problems too expensive for experimental solutions and too complicated for analytical treatment. If the model involves random sampling from a known probability distribution, the procedure is called Monte Carlo Simulation. This is generally computer oriented and is performed as per steps given below: 1. Establish a cumulative distribution function. 2. Set up the table and assign tag numbers, with the help of cumulative distribution function. The Tag numbers are assigned in such a way as to reflect the probability of the various events. It may start with 0 / 00 / 000 or 1/01/001 and end with 9/99/999 or 10/100/1000 respectively as per the number of digits in the probability distribution functions. 3. Obtain the random numbers from a Random Number Generator (RNG). 2.2 Random number generator (RNG): A random number generator (RNG) is a computational or physical device designed to generate a sequence of numbers or symbols that lack any pattern, i.e. appear random. Pseudo-random number generators (PRNGs) are algorithms that can automatically create long runs of numbers with good random properties but eventually the sequence repeats (or the memory usage grows without bound). The string of values generated by such algorithms is 9

10 generally determined by a fixed number called a seed. There are many types Pseudo Random number generators, of which Linear congruential generators(lcg s) is the most commonly used LCG s uses recurrence. Modulus Multiplier Increment Seed are integer constants that specify the generator. The period of a general LCG is at most m, and for some choices of a much less than that. Provided that c is nonzero, the LCG will have a full period for all seed values if and only if 1. and are relatively prime, 2. is divisible by all prime factors of, 3. is multiple of 4 if is a multiple of 4. While LCGs are capable of producing decent pseudorandom numbers, this is extremely sensitive to the choice of the parameters c, m, and a. Random number generation from uniform distribution is done through LCG s. Generation of Random numbers from a probability distribution: There are a couple of methods to generate a random number based on a probability density function. These methods involve transforming a uniform random number in some way. Because of this, these methods work equally well in generating both pseudo-random and true random numbers. For continuous distributions Inversion Method, Rejection Method, Hazard Rate Method can be used. To generate RN s for discrete distributions, Alias method and also analogs methods of continuous distribution can be used. 10

11 Few Matlab codes are constructed for the generating random numbers in different probability distributions using the methods mentioned above Uniform Distribution (generated using LCG between [0,1)) Discrete distributions (generated using inversion method for discrete) A excel file with name discret.xlsx containing probabilities of each event has to be given as input. 11

12 Exponential distribution: (Using Inversion method) For density function of absolute normal variable: (Using Rejection method) 12

13 Normal Distribution: (Using special techniques) All the above RNGs are made from the probability distribution functions. Once a probability distribution function is known random numbers can be generated using any of the standard methods Tests for RNG s: Marsaglia describes a set of tests called Die Hard [3] tests which are used to check the quality of the RNG s. These tests indicated the kinds of possibilities. They are as follows Birthday spacings: Choose m birthdays in a year of n days. List the spacings between birthdays. If j is the number of values that occur more than once in that list, then j has an asymptotic Poisson distribution with mean m 3 /4n. 13

14 Overlapping 5 permutations: Analyse sequences of five consecutive random numbers. The 120 possible orderings should occur with statistically equal probability. Binary rank test for 31x31 matrices: The left most t31 bits of 31 random integers from the test sequence are used to form 31x31 binary matrix. The rank of the matrix is determined. Each time this done, counts are accumulated for matrices with ranks of 31, of 30, of 29 and of 28 or less. A chi- squared test is performed for these four outcomes. Binary rank test for 32x32 matrices: similar to the above test. Binary rank test for 6x8 matrices: similar to the above tests, except the rows of the matrix are specified bytes in the integer words. Bitstream test: using the stream of bits from the RNG, form 20-bit words, beginning with each successive bit, that is, the words overlap. The Bitstream test compares the observed number of missing 20-bit words in a string of 2 21 overlapping 20-bit words with the approximate distribution of that number. Overlapping-pairs-sparse-occupancy test: for this test 2-letter words are formed from an alphabet of 1024 letters. The letters in a word are determined by a specified ten bits from a 32 bit-integer in the sequence to be tested, and the bits defining the letters overlap. The test counts the number of missing words, that is, combinations that do not appear in the entire sequence being tested. The count has asymptotic normal distribution. Overlapping-quadruples-sparse-occupancy test: This is similar to above test. The null distribution of the test is very complicated; interestingly, a parameter of the null distribution of the test statistic was estimated by Monte Carlo. DNA test: this is similar to the tests above, except that it uses 10 letter words built on a 4-letter alphabet (the DNA alphabet). Count the 1 s test: Count the 1 bits in each of either successive or chosen bytes. Convert the counts to "letters", and count the occurrences of fiveletter "words". 14

15 Parking lot test: Randomly place unit circles in a 100 x 100 square. If the circle overlaps an existing one, try again. After 12,000 tries, the number of successfully "parked" circles should follow a certain normal distribution. Minimum distance test: Randomly place large number of points in a square, and then find the minimum distance between the pairs. The square of this distance should be exponentially distributed with the mean dependent on the length of the side of square. 3-D spheres test: Randomly choose 4,000 points in a cube of edge 1,000. Centre a sphere on each point, whose radius is the minimum distance to another point. The smallest sphere's volume should be exponentially distributed with a certain mean. The squeeze test: Multiply 2 31 by random floats on [0,1) until you reach 1. Repeat this 100,000 times. The number of floats needed to reach 1 should follow a certain distribution. Overlapping sums test: Generate a long sequence of random floats on [0,1). Add sequences of 100 consecutive floats. The sums should be normally distributed with characteristic mean and sigma. Runs test: Generate a long sequence of random floats on [0,1). Count ascending and descending runs. The counts should follow a certain distribution. The craps test: Simulate large number of games of craps, counting the wins and the number of throws per game. Each count should follow a certain distribution. 15

16 4. DESIGN OF ALGORITHM 4.1. FOR BRANCH LEVEL SIMULATION MODELLING AND ALM For designing an algorithm for a bank we need to first construct the Algorithm for basic units first. Here the basic unit is branch. Steps for Branch level simulation modelling and ALM are as follows 1. Take input number of days n and the information regarding assets liabilities and interest rate fluctuations. 2. Simulate the data of for a day using Monte-Carlo simulation. And classify the data into buckets. 3. Check whether RBI NORMS are met. If no, then reconstruct bucket structure by disinvesting and investing to satisfy the norms 4. Check for Surplus/deficit. In case of surplus If interest rates increasing - Hold surplus as Inventory If interest rates decreasing - Invest surplus for maximum returns In case of deficit If interest rates increasing - Borrow for long term If interest rates decreasing - Borrow for short term 5. Check whether n is greater than zero or not. If so, go to second step 2 else end the process. Now for the simulation bank assets and liabilities we should use the information from a bank about the deposits and loans and the patterns of their arrival. Due to shortage of time and unavailability of the information from banks, we are using discrete distributions in this demonstration for simplicity. 16

17 Figure (ii) Algorithm for branch simulation modelling and ALM. 17

18 4.2. FOR BANK LEVEL SIMULATION MODELLING AND ALM Bank Branch 1 Branch 2 Branch 3.. Branch k Figure(iii) : simplified view of Bank model. To design an algorithm for Bank Level Simulation and ALM we have to integrate the number of individual branches into single unit. Here we can unify the parameters like assets and liabilities of each branch into one and can make it function as a core model and perform the ALM analysis or we can perform all the ALM analysis on each branch separately. However trying to integrate into a core model is not practical to date and we cannot access performance of each branch in that way. So we prefer the second way of performing analysis. So the changes in the algorithm for a bank are Taking other input for number of branches k And simulating the branch algorithm for k times And the corresponding algorithm design for it is as follows, 18

19 Figure (iv) Algorithm for bank simulation modelling and ALM. 19

20 Based on the above algorithms a Matlab code is designed for the analysis and fed with the following data. Input data Bank deposits: Deposits amount information. Deposits maturity information. Bank Loans: Loans amount Information. Loans maturity information. Inventory of each branch: Inventory information of each branch..* Assumed there are only three branches for the bank. 20

21 Forecast of interest rates: Where 1 indicates increase in interest rates AND -1 indicates decrease in interest rates Forecast is taken for four days and the analysis is also made for four days itself Out Put: Simulation is done based upon the above data. Then all the actions specified are performed on it by the code the final gap structure of each branch and bank are given below and all the remaining details of simulation are kept in annexure. Cumulative gap of 4 days for branch 1. Cumulative gap of 4 days for branch 2. Cumulative gap of 4 days for branch 3. 21

22 Cumulative gap of 4 days for whole Bank. * All the remaining simulated Data and code are kept in the Annexure 4. OBSERVATIONS AND CONCLUSION Analysis is performed on one class of assets (loans) and liabilities (deposits) by considering three parameters like Amount, maturity and forecast of interest rate. For accuracy more parameters can be involved depending on the information from bank. This Tool is now ready to be tested & used by the banking firms for their benefit for performing ALM analysis. If the probability for the occurrence of each scenario (interest rate fluctuations) is known/estimated a stochastic model can be worked out for optimizing the profit. REFERENCES 1. BANK ASSET AND LIABILITY MANAGEMENT (strategy, Trading, Analysis), Moorad Choudary, WILEY FINANCE. Singapore Evolving a Minimum Framework for Assets and liabilities management, P.krishnamurthy, Indian institute of Bankers. Mumbai Random Number Generation and Monte-Carlo Methods, James E. Gentle, Springer. New York An introduction to probability theory and Its Applications (volume I) 3 rd edition, Feller, WSE WILEY. New York