پیش بینی جریان نقد با استفاده از فرایندهای تصادفی پیوسته

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری حسابداری، واحد تهران شمال، دانشگاه آزادسلامی، تهران، ایران.

2 دانشیار، گروه مدیریت مالی، واحد تهران شمال، دانشگاه آزاد اسلامی، تهران، ایران.

3 استادیار، گروه حسابداری، واحد تهران شمال، دانشگاه آزاد اسلامی، تهران، ایران.

4 استادیار، گروه اقتصاد، واحد تهران شمال، دانشگاه آزاد اسلامی، تهران، ایران.

چکیده

از آنجا که وضعیت نقدینگی مبنای قضاوت بسیاری از اشخاص درباره موقعیت واحد اقتصادی است، این مطلب مورد توجه گروه‌های ذینفع از جمله اعتباردهندگان و سرمایه‌گذاران قرارگرفته‌است. هدف این پژوهش درک جدیدی از رفتار جریان نقد و پیش­بینی مانده نقد است. جامعه آماری پژوهش حاضر  مانده نقد روزانه یکساله ۴۸ شعبه بانک معین است. برای این منظور مدل بهینه از بین 4 مدل؛ براونی هندسی، براونی حسابی، واسیسک و مدل ریشه مربعات اصلاح شده در سه سطح میکروسکوپی، مسسکوپی و ماکروسکوپی بررسی گردیده است و مدل براونی هندسی به عنوان مدل بهینه تایید شده است؛ سپس با استفاده از مدل بهینه مذکور پیش‌بینی مانده نقد در افق‌های زمانی متفاوتی صورت‌گرفته‌است. نتیجه نشان می­دهد که قدرت مدلGBM  با افزایش طول افق زمانی پیش­بینی ثابت نمی­ماند و با افزایش افق زمانی پیش­بینی، نتایج متفاوتی دارند صحت پیش­بینی مدل با از معیار MAPEدر افق 14روزه در سطح مناسبی می­باشد. 

کلیدواژه‌ها

عنوان مقاله [English]

Cash flow forecasting using Continuous-Time Stochastic Processes

نویسندگان [English]

  • Elham Danesh 1
  • Ali Saeedi 2
  • Ehsan Rahmani nia 3
  • Amir Gholami 4
1 Ph.D. Candidate in Accounting, North Tehran Branch, Islamic Azad University, Tehran, Iran.
2 Associate Prof., Department of Financial Management, North Tehran Branch, Islamic Azad University, Tehran, Iran.
3 Assistant Prof., Department of Accounting, North Tehran Branch, Islamic Azad University, Tehran, Iran
4 Assistant Prof., Department of Economics, North Tehran Branch, Islamic Azad University, Tehran, Iran.
چکیده [English]


Since the liquidity situation is the basis for many people to judge the position of the economic unit, this issue has been considered by stakeholders including creditors and investors.The purpose of this study is a new understanding of cash flow behavior and cash balance forecasting. The statistical population of the present study is the annual cash balance of 48 branches of a certain bank. For this purpose, the optimal model out of 4 models; Geometric Brownie, Arithmetic Brownie, Vasicek and Modified Square Root Model at three levels of microscopic, mesoscopic and macroscopic have been investigated and the geometric Brownie model has been approved as the optimal model; Then, using the mentioned optimal model, the cash balance is predicted in different time horizons. The result shows that the strength of the GBM model does not remain constant with increasing the length of the forecast time horizon and with increasing the forecast time horizon, they have different results. The accuracy of the model forecast with the MAPE criterion at the 14-day horizon is at an appropriate level.

کلیدواژه‌ها [English]

  • Cash flow
  • Cash balance
  • Stochastic Processes

مراجع

  1. Ait-Sahalia, Y. Jacod, J, (2010), Is Brownian Motion Necessary to Model High Frequency Data?, The Annals of Statistics, 38, 3093-3128.
  2. Alexander, D. R., Mo, M., & Stent, A. F. (2012). Arithmetic Brownian motion and real options. European Journal of Operational Research, 219(1), 114-122.
  3. Bartlett, M. S. (1955). An introduction to stochastic processes: with special references to methods and applications: Cambridge University Press.
  4. Basel Committee on Banking supervision (2000), Sound Practices for Managing Liquidity in Banking  Organisations.
  5. Bergstrom, A. R. (1990). Continuous time econometric modelling: Oxford University Press, Incorporated.
  6. Bhattacharya, S. (1978). PROJECT VALUATION WITH MEAN-REVERTING CASH FLOW STREAMS. The Journal of Finance, 33(5), 1317-1331.
  7. Cox, D. R., & Miller, H. D. (1977). The Theory of Stochastic Processes: Taylor & Francis.
  8. Davallo. M, Varzideh.A.R. (2020). Forcasting total index of Tehran Stock Exchange using Geometric Brownian motion model. Financial Knowledge of Securities Analysis, 13( 46), 193-208. (In Persian)
  9. Davoodi,S.M.R ,& Mirsaeedi, K.(2019). The Analysis of the Tehran Stock Exchange Index in the Framework of Markov Chains, Journal of Financial Management, Perspective .25, 31-57. (In Persian)
  10. Doob, J. L. (1990). Stochastic processes: Wiley
  11. Dreman D. and M. Berry. (1995). Overreaction, Underreaction and the Low-P/E Effect. Financial Analysts Journal ,51(4): 21-30
  12. Feller, W. (1971). An Introduction to Probability Theory and Its Applications: Wiley.
  13. Fuchs, C. (2013). Inference for Diffusion Processes: With Applications in Life Sciences: Springer Berlin Heidelberg.
  14. Gandolfo, G. (2012). Continuous-Time Econometrics: Theory and applications: Springer Netherlands.
  15. Gillespie, D. T. (1992). Markov Processes: An Introduction for Physical Scientists: Academic Press.
  16. Gardiner, C. W. (1985). Handbook of stochastic methods for physics, chemistry, and the natural sciences: Springer-Verlag.
  17. Handan ,Jarr,Z. Ibrahim, S.I , Mustafa , A.M.S.(2020). Modelling Alaysian Gold Prices Using Geometric Brownian Motion Model. Advances in Mathematics: Scientific Journal, 9 (45), 7463–7469.
  18. Karlin, S., & Taylor, H. E. (2012). A First Course in Stochastic Processes: Elsevier Science.
  19. Karlin, S., & Taylor, H. M. (1981). A Second Course in Stochastic Processes: Academic Press.
  20. Kotelenez, P. (2007). Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations: Springer New York.
  21. Klumpes, P., & Tippett, M. (2004). A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis) invest. Journal of Business Finance & Accounting, 31(9-10), 1449-1481
  22. Lindeberg, J. W. (1922). Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung. Mathematische Zeitschrift, 15(1), 211-225.
  23. Molaei, S. Baezani ,M.V. Samadi,S(2016). Modeling behavior of stock price using stochastic differential equations vollidity . Journal of Financial Knowledge, Securities Analysis, 9 (32), 1-13.(In Persian)
  24. Omar, A., & Jaffar, M. M. (2011). Comparative analysis of Geometric Brownian motion model in forecasting FBMHS and FBMKLCI index in Bursa Malaysia. In Business, Engineering and Industrial Applications. (ISBEIA), IEEE Symposium on (pp. 157-161).
  25. ow,R. & Protter,P.(2004) .A short history of stochastic integration and mathematical finance: The early years, 1880–1970. A Festschrift for Herman Rubin Institute of Mathematical Statistics Lecture Notes – Monograph Series.
  26. Rafei, M., Karimi shoushtari, M. (2020). Investigation of Efficiency of Stochastic Differential Equations Driven by Levy Process in Modeling of Exchange Rate Volatility (COGARCH Approach). Applied Economics Studies, Iran (AESI), 8(32), 81-101. (In Persion)
  27. Risken, H., & Frank, T. (2012). The Fokker-Planck Equation: Methods of Solution and Applications: Springer Berlin Heidelberg.
  28. Sadeqi.H, Fadaeinejad, M.E. Varzideh .A.R. (2019). Application of Geometric Brownian motion in predicting gold price and exchange rate. Journal of Investment Knowledge. 8( 30), 251-270. (In Persian)
  29. Saeedi,A.,& Shabani .M.,(2010). To Assess Banking Liquidity Risk by Emery’s Lambda .Quarterly Journal of the Stock Exchange Organization . 3 (3) 3, 129-149. (In Persian)
  30. Salas-Molina, F., Martin, F.J., Rodr´ıguez-Aguilar, J.A.(2018), Empirical analysis of daily cash flow time-series and its implications for forecasting. SORT. 42 (1) , 73-98.
  31. Shivaie, E., Jalaee Esfandabadi, S. A.M., Salehi Esfiji, N. (2018).Modeling exchange rate behavior in Iran using random differential equations: Merton model and NGARCH Approach, Applied Economics Studies, Iran (AESI), 7( 27), 1-21. (In Persian)
  32. Tari Wardi,Y.Amraei,H & Mehdipooor Roshan,S. (2016). Investigating the effect of operating profit, financial leverage and size on liquidity Companies listed on the Tehran Stock Exchange, Journal of Financial Management Perspective,5 (11), 83-106. (In Persian)
  33. Tong,C., and chen,S. (2009). Parameter Estimation and Bias Correletion of Diffiuasion Prosses. Journal of Economecrics ,149(1) , 65-81.
  34. Van Kampen, N. G. (2011). Stochastic Processes in Physics and Chemistry: Elsevier Science.
  35. Van der Burg, J. G. (2018). Stochasthic Continos-Time Cash Flows ,A Copled Linear-Quadratic Model. A Thesise for the degree of Doctor of  Philosophy. Victoria University of Wellington.
  36. Van der Burg, J. G. (2015). Do Firms’ Free Cash Flow Movements Fit Arithmetic Brownian Motion? Evidence from the New Zealand Capital Market. Research Paper.
  37. Yang, Z. a. S., Dandan and Yang, Jinqiang. (2011). The Pricing and Timing of the Option to Invest for Cash Flows with Partial Information Available at SSRN: http://ssrn.com/abstract=1734302 or http://dx.doi.org/10.2139/ssrn.1734302
  38. Zandieh,M.& Khami,M.(2015). Predict stock prices using a combination of the hidden Markov model and the Markov chain, Journal of Financial Management Perspective .12, 27-40. (In Persian)
  39. Wattaatorn, W. , & Sombultawee, K ., (2021). The Stochastic Volatility Option Pricing Model: Evidence from a Highly Volatile Market. Journal of Asian Finance, Economics and Business.8 (2), 0685–0695.
چشم انداز مدیریت مالی
دوره 12، شماره 37
فروردین 1401
صفحه 123-145

فایل ها

هم رسانی

ارجاع به این مقاله

آمار