Daily net cash flow analysis and forecasting : Transition from Microscopic to Macroscopic Stochastic Equations

Advances in Mathematical Finance and Applications

مقاله 2، دوره 8، شماره 4، آذر 2023، صفحه 1111-1123   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/amfa.2022.1942773.1643

نویسندگان

Elham Danesh¹؛ Ali Saeedi^{* 2}؛ Ehsan Rahmaninia¹؛ Amir Gholami³

¹Department of Accounting, North Tehran Branch, Islamic Azad University, Tehran, Iran

²Department of Financial Management, North Tehran Branch, Islamic Azad University, Tehran, Iran

³Department of Economics, North Tehran Branch, Islamic Azad University, Tehran, Iran.

چکیده

The purpose of this study is a new understanding behaviour and net cash flow forecasting. The data of this research contains the daily trial balance for one year, which has been received from 48 bank branches. For this purpose, the optimal model out of 4 models; Geometric Brownie, Arithmetic Brownie, Vasicek and Modified Square Root at three levels of microscopic, mesoscopic and macroscopic have been investigated and the Geometric Brownie model has been approved as the optimal model in microscopic level . The results show that Geometric Brownian Motion model can simulate the net cash flow highly accurate in accordance with the criteria of mean absolute percentage error. also forecasting net cash flow for each under study time series has been done in various forecasting horizons involved 7, 14, 21, 30, 60, 90 and 180 day time period accordance with the criteria of mean absolute percentage error. Also The other results obtained from this study is that according to 8 different prediction accuracy criteria, By increasing the forecast hori-zon, ability of the GBM model in simulation and forecasting the net cash flow de-creases.

کلیدواژه‌ها

Net cash flow؛ Geometric Brown Motion؛ Arithmetic Brownian Motion؛ Vasicek؛ Modified Square Root

مراجع

[1] Basel Committee on Banking supervision, Sound of Practices for Managing Liquidity in Banking Organizations, BIS, February ,2000.

 

[2] Corsaro, S., Kyriakou, I., Marazzina, D., and Marino, Z.A., General Framework for Pricing Asian Options under Stochastic Volatility on Parallel Architectures, European Journal of Operational Research Volume, 2019, 272(3), P. 082-1095. Doi.org/10.2139/ssrn.3331550

 

[3] Cox, C., Ingersoll, J.E, Ross, S, A., A Theory of the Term Structure of Interest Rates, Econometrica, 1985, 53(2), P.385-407. Doi:10.2307/1911242

 

[4] Davallo. M., Varzideh, A.R., Forecasting total index of Tehran Stock Exchange using Geometric Brownian motion model, 2020, 13(46), P.193-208. (In Persian)

 

[5] Fathi Vajarga, K., Eslami Mofid Abadi, H., Abbasi, E., Oil Price Estimating under Dynamic Economic Models Using Markov Chain Monte Carlo Simulation   Approach, Advances in Mathematical Finance and Applications, 2020, 6(3), P.631-651. Doi: 10.22034/AMFA.2020.1902265.1446

 

[6] Ghanbari, M., Goldani, M., Support Vector Regression Parameters Optimization using Golden Sine Algorithm and its Application in Stock Market. Advances in Mathematical Finance and Applications, 2022, 7(2), P. 327-343. Doi: 10.22034/AMFA.2021.1936352.1623

 

[7] Izadikhah, M., A Fuzzy Goal Programming Based Procedure for Machine Tool Selection, 2015, 28(1), P. 361-372, Doi: 10.3233/IFS-141311

[8] Handan, Z., Ibrahim, S.I., and Mustafa, A.M.S., Modelling Alaysian Gold Prices Using Geometric Brownian Motion Model, Advances in Mathematics: Scientific Journal, 2020, 9(20), P.7463–7469. Doi: 10.37418/amsj.9.9.92

[9] Klumpes, P., Tippett, M., A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis) invest, Journal of Business Finance & Accounting, 2004, 31(9-10), P.1449-1481.  Doi:10.1111/j.0306-686X.2004. 00580.x  

 

[10] Kotelenez, P., Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations: Springer New York, 2007.

 

[11] Lawrence, K. D., Klimberg, R. K., Lawrence, S. M., Fundamentals of forecasting using excel, Industrial Press Inc, 2009.

 

[12] Sadeghi, H, Fadaeineghad, M.E., Varzideh, A.R., Application of geometric Brownian motion in predicting gold price and exchange rate, Sientific and Reaserch Journals management system, 2019, 8(30), P.251-270. (In Persian)

 

[13] Saeedi, A., Shabani, M., To Assess Banking Liquidity Risk by Emery’s Lambda. Quarterly Journal of the Stock Exchange Organization. 2010 ,3 (3), 129-149. (In Persian)

 

[14] Salas-Molina, F., Martin, F.J., and Rodr´ıguez-Aguilar, J.A., Empirical analysis of daily cash flow time-series and its implications for forecasting, International Journal of Forecasting, 2018 ,42 (1), P. 73-98. Doi:10.48550/arXiv.1611.04941

 

[15] Talebi, B., Abdi, R., Hajiha,Z., Rezaei, N., The Evaluation of the Capability of the Regression and Neural Network Models in Predicting Future Cash Flows. Advances in Mathematical Finance and Applications, 2022, 7(2), P. 327-343. Doi: 10.22034/AMFA.2020.1876840.1277

 

[16] Tong, C., Chen, S., Parameter Estimation and Bias Correletion of Diffiuasion Prosses, Journal of Economecrics, 2009, 149(1), P.65-81. Doi: 10.1016/J.JECONOM.2008.11.001

 

 [17] Omar, A., Jaffar, M. M., Comparative analysis of Geometric Brownian motion model in forecasting FBMHS and FBMKLCI index in Bursa Malaysia. In Business, Engineering and Industrial Applications (ISBEIA), 2011, P. 157-161. Doi:10.1109/ISBEIA.2011.6088794

 

[18] Zanjirdar, M., Kasbi, P., Madahi, Z., Investigating the effect of adjusted DuPont ratio and its components
on investor & quot; s decisions in short and long term, Management Science Letters, 2014, 4(3), P.591-596.
Doi: 10.5267/j.msl.2014.1.003

[19] Primbs J. A., Barmish. R.B., On Robustness of Simultaneous Long-Short Stock Trading Control with Time-Varying Price Dynamics, IFAC-Papers On Line, 2018, 50(1), P.12267-12272.

Doi: 10.1016/j.ifacol.2017.08.2045

 

[20] Van der Burg, J.G., Stochastic Continuous-Time Cash Flows, A Coupled Linear-Quadratic Model. P.h.D Thesis, Victoria University, Wellington, New Zealand, 2018.

 

[21] Watttorn, W., Sombultawee, K., The Stochastic Volatility Option Pricing Model: Evidence from a Highly Volatile Market, Journal of Asian Finance, Economics and Business, 2021, 8(2), P.0685–0695.

Doi: 10.13106/JAFEB.2021.VOL8.NO2.0685