A calibration procedure for analyzing stock price dynamics in an agent-based framework. (English) Zbl 1401.91564
Summary: In this paper we introduce a calibration procedure for validating of agent based models. Starting from the well-known financial model of W. A. Brock and C. H. Hommes [J. Econ. Dyn. Control 22, No. 8–9, 1235–1274 (1998; Zbl 0913.90042)], we show how an appropriate calibration enables the model to describe price time series. We formulate the calibration problem as a nonlinear constrained optimization that can be solved numerically via a gradient-based method. The calibration results show that the simplest version of the Brock and Hommes model, with two trader types, fundamentalists and trend-followers, replicates nicely the price series of four different markets indices: the S&P 500, the Euro Stoxx 50, the Nikkei 225 and the CSI 300. We show how the parameter values of the calibrated model are important in interpreting the trader behavior in the different markets investigated. These parameters are then used for price forecasting. To further improve the forecasting, we modify our calibration approach by increasing the trader information set. Finally, we show how this new approach improves the models ability to predict market prices.
MSC:
| 91G70 | Statistical methods; risk measures |
| 91B69 | Heterogeneous agent models |
| 91G80 | Financial applications of other theories |
Keywords:
calibration; validation; forecasting; agent-based models; asset pricing; heterogeneous beliefsCitations:
Zbl 0913.90042Software:
mebootReferences:
| [1] | Alfarano, S.; Lux, T.; Wagner, F., Estimation of agent-based modelsthe case of an asymmetric herding model, Comput. Econ., 26, 1, 19-49, (2005) · Zbl 1161.91364 |
| [2] | Alfarano, S.; Lux, T.; Wagner, F., Estimation of a simple agent-based model of financial marketsan application to Australian stock and foreign exchange data, Phys. A, 370, 1, 38-42, (2006) |
| [3] | Alfarano, S.; Lux, T.; Wagner, F., Empirical validation of stochastic models of interacting agents, Eur. Phys. J. B, 55, 2, 183-187, (2007) · Zbl 1189.91103 |
| [4] | Andersen, L.; Andreasen, J., Jump diffusion modelsvolatility smile Fitting and numerical methods for pricing, Rev. Deriv. Res., 4, 231-262, (2000) · Zbl 1274.91398 |
| [5] | Avellaneda, M.; Buff, R.; Friedman, C.; Grandchamp, N.; Kruk, L.; Newman, J., Weighted Monte carloa new technique for calibrating asset-pricing models, Int. J. Theor. Appl. Financ., 4, 1, 91-119, (2001) · Zbl 1153.91458 |
| [6] | Bannerjee, A. V., A simple model of herd behavior, Q. J. Econ., 107, 797-817, (1992) |
| [7] | Bannerjee, A. V., The economics of rumors, Rev. Econ. Stud., 60, (1993) · Zbl 0775.90094 |
| [8] | Bates, D. S., Jumps and stochastic volatilitythe exchange rate processes implicit in deutschemark options, Rev. Financ. Stud., 9, 1, 69-107, (1996) |
| [9] | Bentley, K.; Gerhardt, H.; Bates, P. A., Agent-based simulation of notch mediated tip cell selection in angiogenic sprout initialisation, J. Theor. Biol., 250, 1-25, (2009) |
| [10] | Bentley, K.; Jones, M.; Cruys, B., Predicting the futuretowards symbiotic computational and experimental angiogenesis research, Exp. Cell Res., 3, 19, 1240-1246, (2013) |
| [11] | Bianchi, C.; Cirillo, P.; Gallegati, M.; Vagliasindi, P., Validating and calibrating agent-based modelsa case study, Comput. Econ., 30, 245-264, (2007) · Zbl 1310.91116 |
| [12] | Bianchi, C.; Cirillo, P.; Gallegati, M.; Vagliasindi, P., Validation in agent-based modelsan investigation on the CATS model, J. Econ. Behav. Organ., 67, 947-964, (2008) |
| [13] | Boswijk, H. P.; Hommes, C.; Manzan, S., Behavioral heterogeneity in stock prices, J. Econ. Dyn. Control, 31, 6, 1938-1970, (2007) · Zbl 1201.91223 |
| [14] | Brock, W. A.; Hommes, C. H., A rational route to randomness, Econometrica, 65, 1059-1095, (1997) · Zbl 0898.90042 |
| [15] | Brock, W.A., Hommes, C.H., 1997b. Models of complexity in economics and finance. In: Hey, C., et al. (Eds.), System Dynamics in Economic and Financial Models. Wiley Publications, New York, USA, pp. 3-41. |
| [16] | Brock, W. A.; Hommes, C. H., Heterogeneous beliefs and routes to chaos in a simple asset pricing model, J. Econ. Dyn. Control, 22, 1235-1274, (1998) · Zbl 0913.90042 |
| [17] | Chen, B.; Pearl, J., Regression and causation: a critical examination of six econometrics textbooks, Real-World Econ. Rev., 65, 2-20, (2013) |
| [18] | Chiarella, C.; Iori, G.; Perello, J., The impact of heterogeneous trading rules on the limit order book and order flows, J. Econ. Dyn. Control, 33, 3, 525-553, (2009) · Zbl 1170.91371 |
| [19] | Cirillo, P.; Gallegati, M., The empirical validation of an agent-based model, East. Econ. J., 38, 525-547, (2011) |
| [20] | Cont, R., Volatility clustering in financial marketsempirical facts and agent-based models, Long Memory in Economics, 289-309, (2007), Springer Berlin, Heidelberg · Zbl 1181.91341 |
| [21] | Delli Gatti, D.; Gallegati, M.; Greenwald, B.; Russo, A.; Stiglitz, J., Mobility constraints, productivity trends, and extended crises, J. Econ. Behav. Organ., 83, 375-393, (2012) |
| [22] | Delli Gatti, D., Desiderio, S., Gaffeo, E., Cirillo, P., Gallegati, M., 2011. Macroeconomics from the Bottom-Up. Ed: Springer, Netherlands; Series: New Economic Windows. · Zbl 1269.91001 |
| [23] | Fatone, L.; Mariani, F.; Recchioni, M. C.; Zirilli, F., The analysis of real data using a multiscale stochastic volatility model, Eur. Financ. Manag. J., 19, 1, 153-179, (2013) |
| [24] | Fagiolo, G.; Birchenhall, C.; Windrum, P., Special issue on empirical validation in agent-based models, Comput. Econ., 30, 3, 30, (2007) |
| [25] | Fouque, J. P.; Papanicolaou, G.; Sircar, R., Derivatives in financial markets with stochastic volatility, (2001), Cambridge University Press New York, USA |
| [26] | Fusai, G.; Roncoroni, A., Implementing models in quantitative financemethods and cases, Springer Finance, (2008), Springer-Verlag Berlin · Zbl 1213.91008 |
| [27] | Gaunersdorfer, A.; Hommes, C. H.; Wagener, F. O.O., Bifurcation routes to volatility clustering under evolutionary learning, J. Econ. Behav. Organ., 67, 27-47, (2008) |
| [28] | Gilli, M.; Winker, P., A global optimization heuristic for estimating agent-based models, Comput. Stat. Data Anal., 42, 299-312, (2003) · Zbl 1429.65123 |
| [29] | Hadavandi, E.; Ghanbari, A.; Abbasian-Naghneh, S., Developing an evolutionary neural network model for stock index forecasting, Adv. Intell. Comput. Theor. Appl. Commun. Comput. Inf. Sci., 93, 407-415, (2010) · Zbl 1210.68081 |
| [30] | Hansen, L. P.; Heckman, J. J., The empirical foundations of calibration, J. Econ. Perspect., 10.1, 87-104, (1996) |
| [31] | Hassan, S.; Arroyo, J.; Galán, J. M.; Antunes, L.; Pavón, J., Asking the oracleintroducing forecasting principles into agent-based modelling, J. Artif. Soc. Soc. Simul., 16, 3, 13, (2013), http://jasss.soc.surrey.ac.uk/16/3/13.html |
| [32] | Hommes, C., Financial markets as nonlinear adaptive evolutionary systems, Quant. Financ., 1, 1, 149-167, (2001) · Zbl 1405.91624 |
| [33] | Hommes, C., 2006. Heterogeneous agent models in economics and finance. In: Leigh Tesfatsion, Kenneth L. Judd (Eds.). Handbook of Computational Economics, vol. 2. Elsevier B.V., Netherlands, 〈http://dx.doi.org/10.1016/S1574-0021(05)02023-X.〉 |
| [34] | LeBaron, B.; Arthur, W. B.; Palmer, R., Time series properties of an artificial stock market, J. Econ. Dyn. Control, 23, 1487-1516, (1999) · Zbl 0959.91017 |
| [35] | LeBaron, B. 2006. Agent-based computational finance. In: Leigh Tesfatsion, Kenneth L. Judd (Eds.). Handbook of Computational Economics, Elsevier B.V.,Netherlands · Zbl 1143.91300 |
| [36] | LeBaron, B.; Yamamoto, R., Long-memory in an order-driven market, Phys. A, 383, 1, 85-89, (2007) |
| [37] | LeBaron, B.; Yamamoto, R., The impact of imitation on long memory in an order-driven market, East. Econ. J., 34, 4, 504-517, (2009) |
| [38] | Liu, L.M., 2009. Time Series Analysis and Forecasting, Second ed., Scientific Computing Associates Corp., U.S.A., ISBN: 978-0-9765056-8-6. |
| [39] | Lux, T.; Marchesi, M., Volatility clustering in financial marketsa micro simulation of interacting agents, Int. J. Theor. Appl. Financ., 3, (2000) · Zbl 0967.91072 |
| [40] | Mancino, M. E.; Sanfelici, S., Estimation of quarticity with high-frequency data, Quant. Financ., 12, 4, 607-622, (2012) · Zbl 1278.91197 |
| [41] | Midgley, D. F.; Marks, R. E.; Cooper, L. G., Breeding competitive strategies, Manag. Sci, 43, 3, 257-275, (1997) · Zbl 0900.90367 |
| [42] | Muth, J. F., Rational expectations and the theory of price movements, Econometrica, 29, 315-335, (1961) |
| [43] | Nielsen, M. O.; Frederiksen, P., Finite sample accuracy and choice of sampling frequency in integrated volatility estimation, J. Empir. Financ., 15, 265-286, (2007) |
| [44] | Orhangazi, O., Financialization and capital accumulation in the non-financial corporate sector, Camb. J. Econ., 32, 6, 863-886, (2008) |
| [45] | Preethi, G.; Santhi, B., Stock market forecasting techniquesa survey, J. Theor. Appl. Inf. Technol., 46, 1, 24-30, (2012) |
| [46] | Ponta, L.; Raberto, M.; Cincotti, S., A multi-assets artificial stock market with zero-intelligence traders, Europhys. Lett., 93, 28002, (2011) |
| [47] | Raberto, M.; Cincotti, S.; Focardi, S. M.; Marchesi, M., Agent-based simulation of a financial market, Phys. AStat. Mech. Appl., 299, 1, 319-327, (2001) · Zbl 0974.91013 |
| [48] | Raberto, M.; Cincotti, S.; Focardi, S. M.; Marchesi, M., Traders׳ long-run wealth in an artificial financial market, Comput. Econ., 22, 2, 255-272, (2003) · Zbl 1062.91578 |
| [49] | Recchioni, M. C.; Scoccia, A., A stochastic algorithm for constrained global optimization, J. Global Optim., 16, 257-270, (2000) · Zbl 0962.90038 |
| [50] | Rochon, L. P.; Rossi, S., Has ‘it’ happened again, Int. J. Polit. Econ., 28, 4, 832-862, (2010) |
| [51] | Sims, C. A., Macroeconomics and methodology, J. Econ. Perspect., 10, 105-120, (1996) |
| [52] | Tedeschi, G.; Iori, G.; Gallegati, M., The role of communication and imitation in limit order markets, Eur. Phys. J. B, 1, 489-497, (2009), http://www.springerlink.com/content/4104048222065m17 · Zbl 1188.91163 |
| [53] | Tedeschi, G.; Iori, G.; Gallegati, M., Herding effects in order driven marketsthe rise and fall of gurus, J. Econ. Behav. Organ., 81, 82-96, (2012) |
| [54] | Teräsvirta, T., Specification, estimation, and evaluation of smooth transition autoregressive models, J. Am. Stat. Assoc., 89, 208-218, (1994) · Zbl 1254.91686 |
| [55] | Tesfatsion, L., 2013. Website on Validation of ACE: 〈http://www.econ.iastate.edu/tesfatsi/empvalid.htm〉. |
| [56] | Troitzsch, K., 2004. Validating simulation models. In: Proceedings of the 18th European Simulation Multiconference, SCS Europe, pp. 98-106. |
| [57] | Vinod, H. D.; Lòpez-de-Lacalle, J., Maximum entropy bootstrap for time series. the meboot R package, J. Stat. Softw., 29, 1-19, (2009) |
| [58] | Wells, C., 1996. The Kalman Filter in Finance. Advanced Studies in Theoretical and Applied Econometrics, vol. 32, Kluwer Academic Publishers, Netherlands. |
| [59] | Winker, P., Gilli, M., 2001. Indirect estimation of the parameters of agent based models of financial markets. Technical Report 03/2001, School of Business Administration, International University in Germany, Bruchsal. |
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