Futures Valuation Beased on Stochastic Interest Rate in Iran Mercantile Exchange

Subject Areas : Financial engineering

Moslem Peymany Foroushany ¹ , Meysam Amiri ² , Ali Rajabloo ³

1 - Assistant Professor, Department of Finance and Banking, Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran
2 - Assistant Professor, Department of Finance and Banking, Faculty of Management and Accounting, Allameh Tabataba’i University, Tehran, Iran
3 - Master's degree student, Department of Financial Engineering and Risk Management, Faculty of Management and Accounting, Allameh Tabatabai University, Tehran, Iran

Received: 2024-03-19 Accepted : 2024-09-19 Published : 2024-12-24

Keywords: Futures Contract, Stochastic Interest Rate, Vasicek Model, CIR Model, RMSE ,

Abstract :

One of the widely used tools in risk management and portfolio optimization is derivatives. Future contracts are one of the most important derivative instruments that are used by investors and risk hedgers.In recent years, with the increase in the volume and value of the futures market transactions, the attractiveness of this market for economic operators has increased significantly.The purpose of this research is the valuation of the futures contract based on stochastic interest rate models and compare their performance with the valuation model under non-stochastic interest rate in Iran Mercantile Exchange.In this research, using the stochastic interest rate models of Vasicek (1977) and Cox, Ingersoll and Ross (1985), we value future contracts in the Iran Mercantile Exchange from the March 2021 to the August 2022. The data of futures contracts are divided into short-term and long-term groups based on the remaining time to maturity; As a result, based on the RMSE criterion and then the variance analysis test of the valuation results, it was found that there is no significant difference between the valuation models in the valuation of short-term contracts, while the valuation under the Vasicek model of long-term contracts and all contracts, performed better than other models.

References:

آذر, ‌عادل, کریمی, ‌سیروس. (1388). پیش‌بینی بازده سهام با استفاده از نسبت‌های حسابداری با رویکرد شبکه‌های عصبی. تحقیقات مالی, 20-3,. (1)28
پیمانی, مسلم, هوشنگی, زهره. (1396).تخمین و مقایسه مدل‌های تعادلی نرخ سود کوتاه‌مدت اسناد خزانه اسلامی .مهندسی مالی و مدیریت اوراق بهادار, 111-89 .، (33)8
خبیری، علی (1395).مطالعه تجربی بازار قراردادهای آتی کالا.رساله دکتری.دانشگاه تهران
خسروی, مهرجو, محسنی. (1393). نقش بازار مالی و سرمایه‌گذاری مستقیم خارجی بر رشد اقتصادی بخش کشاورزی-رهیافت داده‌های ترکیبی پویا. فصلنامه علمی-پژوهشی تحقیقات اقتصاد کشاورزی, 130-103,.(21)6
صفائی، مریم، نیسی، عبدالساده، و نعمت الهی، نادر. (1397). یک روش عددی برای حل مساله قیمت گذاری اختیارات آمریکایی تحت مدل نرخ بهره تصادفی CIR. مهندسی مالی و مدیریت اوراق بهادار (مدیریت پرتفوی)، 9(35 )، 259-281.
کارنامه حقیقی، مهدی (1390) قیمت‌گذاري نظري قراردادهاي آتی در چارچوب مدل فرآیندهاي تصادفی : موردمطالعه قرارداد آتی سکه طلا. پایان‌نامه کارشناسی ارشد. دانشگاه اصفهان
ملک محمدی، سارا (1399). مقایسه عملکرد مدل‌های ارزش‌گذاری اوراق اختیار معامله در بورس اوراق بهادار تهران. پایان‌نامه کارشناسی ارشد. دانشگاه علامه طباطبائی.
مهمان‌دوست، نسترن(1395). بررسی پويايی قیمت نفت و ارزيابی قراردادهای آتی نفت. پایان‌نامه کارشناسی ارشد ریاضی.دانشگاه خوارزمی.
موسوی، حبیب(1391). بررسي روش‌های قيمت‌گذاري قراردادهاي آتي سکه بهار آزادي در بورس کالاي ايران.پایان‌نامه کارشناسی ارشد.دانشگاه علوم اقتصادی.

Figlewski, S. (1984). Hedging performance and basis risk in stock index futures. The Journal of Finance, 39(3), 657-669.
Munk, C. (2011). Fixed income modelling. Oxford University Press‏ Acharya, V. V., Brenner, M., Engle, R. F., Lynch, A. W., & Richardson, M. (2009). Derivatives the ultimate financial innovation. Restoring financial stability: How to repair a failed system, 233, 241

Azar, A., & Karimi, S. (2010). Neural Network Forecasts of Stock Return Using Accounting Ratios. Financial Research Journal, 11(28). (in Persian)
Bhatt, S., & Cakici, N. (1990). Premiums on stock index futures-some evidence. The Journal of Futures Markets (1986-1998), 10(4), 367
Brooks, C. (2019). Introductory econometrics for finance. Cambridge university press Chen, J., Ewald, C., Ouyang, R., Westgaard, S., & Xiao, X. (2022). Pricing commodity futures and determining risk premia in a three factor model with stochastic volatility: the case of Brent crude oil. Annals of Operations Research, 313(1), 29-46

Cornell, B., & French, K. R. (1983). Taxes and the pricing of stock index futures. The Journal of Finance, 38(3), 675-694
Cortazar, G. and Naranjo, L. (2006), “An N-Factor Gaussian Model of Oil Futures Prices”, Journal of Futures Markets, 26, 243-268 Cortazar, G., & Schwartz, E. S. (1997). Implementing a real option model for valuing an undeveloped oil field. International Transactions in Operational Research, 4(2), 125–137

Cox, J. Ingersoll, J. Ross, S. (1985). “A Theory of the Term Structure of Interest Date, P., Mamon, R., & Tenyakov, A. (2013). Filtering and forecasting commodity futures prices under an HMM framework. Energy Economics, 40, 1001–1013
Elton, E. J., Gruber, M. J., & Rentzler, J. (1984). Intra-day tests of the efficiency of the treasury bill futures market. The Review of Economics and Statistics, 129-137

Hull, J. C. (2021). Option, Futures, and Other Derivatives: Eleventh Edition . New York: Pearson Karnamehaghighi, M.(2011). Theoretical Pricing of Future Contracts in Stochastic Processes Model Framework: Case Study Gold Coin. University of
Isfahan , Iran. (in Persian) KH, M., M, S., & M, R. (2014). The Effect of Financial Market and FDI upon Economic Growth of Agricultural Sector: GMM Approach. Agricultural
Economics Research, 6(21), 103-130. (in Persian)
Khabiri, A. (2017). An Empirical Study of Commodity Futures Market. University of Tehran , Iran. (in Persian)
Kwok, Y. K. (2008). Mathematical models of financial derivatives. Springer Malekmohamadi, S. (2021). Performance Comparison of Option Pricing Models in Tehran Stock Exchange. Allameh Tabataba’i University, Iran. (in Persian)

Mehmandoost, N. (2017). The Dynamics of Oil Prices and Valuation of Oil Futures. University of kharazmi , Iran. (in Persian) Modest, D. M., & Sundaresan, M. (1983). The relationship between spot and futures prices in stock index futures markets: Some preliminary evidence. The Journal of Futures Markets (pre-1986), 3(1), 15

Moosavi, H. (2012). A study on the Gold coin future contracts pricing model in Iran Mercantile Exchange. University of kharazmi , Iran. (in Persian) Neisy, A., Safaei, M., & Nematollahi, N. (2018). A Numerical method for solving the problem of Pricing American Options under the CIR stochastic interest rate model. Financial Engineering and Portfolio Management, 9(35), 259-281. (in Persian)
Peymany, M., & Hooshangi, Z. (2017). Estimation and Comparison of ShortTerm Interest Rate Equilibrium Models Using Islamic Treasury Bills. Financial Engineering and Portfolio Management, 8(33), 89-111. (in Persian)

Schröder, M. (1989). Computing the constant elasticity of variance option pricing formula. The Journal of Finance, 44(1), 211–219
Schwartz, E. S. (1997). The stochastic behavior of commodity prices: Implications for valuation and hedging. The Journal of Finance, 52(3), 923–973