Calibrating the Mean-Reversion Parameter in the Hull-White Model Using Neural Networks
Interest rate models are widely used for simulations of interest rate movements and pricing of interest rate derivatives. We focus on the Hull-White model, for which we develop a technique for calibrating the speed of mean reversion. We examine the theoretical time-dependent version of mean reversion function and propose a neural network approach to perform the calibration based solely on historical interest rate data. The experiments indicate the suitability of depth-wise convolution and provide evidence for the advantages of neural network approach over existing methodologies. The proposed models produce mean reversion comparable to rolling-window linear regression’s results, allowing for greater flexibility while being less sensitive to market turbulence.
KeywordsNeural networks Time-dependent mean-reversion Calibration Interest rate models Hull-White model
This project has received funding from Sofoklis Achilopoulos foundation (http://www.safoundation.gr/) and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement no. 675044 (http://bigdatafinance.eu/), Training for Big Data in Financial Research and Risk Management.
- 1.BIS: Over-the-counter derivatives statistics. https://www.bis.org/statistics/derstats.htm. Accessed 05 Feb 2018
- 3.Suarez, E.D., Aminian, F., Aminian, M.: The use of neural networks for modeling nonlinear mean reversion: measuring efficiency and integration in ADR markets. IEEE (2012)Google Scholar
- 7.Exley, J., Mehta, S., Smith, A.: Mean reversion. In: Finance and Investment Conference, pp. 1–31. Citeseer (2004)Google Scholar
- 8.Narayanan, H., Mitter, S.: Sample complexity of testing the manifold hypothesis. In: Advances in Neural Information Processing Systems, vol. 23, Curran Associates Inc., Red Hook (2010)Google Scholar
- 9.Wei, L.-Y., Cheng, C.-H.: A hybrid recurrent neural networks model based on synthesis features to forecast the Taiwan stock market. Int. J. Innov. Comput. Inf. Control 8(8), 5559–5571 (2012)Google Scholar
- 10.Hernandez, A.: Model calibration with neural networks. Risk.net, July 2016Google Scholar
- 11.Gurrieri, S., Nakabayashi, M., Wong, T.: Calibration methods of Hull-White model, November 2009. https://doi.org/10.2139/ssrn.1514192
- 12.Sepp, A.: Numerical implementation of Hull-White interest rate model: Hull-white tree vs finite differences. Technical report, Working Paper, Faculty of Mathematics and Computer Science, Institute of Mathematical Statistics, University of Tartu (2002)Google Scholar
- 13.Tsantekidis, A., Passalis, N., Tefas, A., Kanniainen, J., Gabbouj, M., Iosifidis, A.: Forecasting stock prices from the limit order book using convolutional neural networks. IEEE (2017)Google Scholar
- 14.Luo, R., Zhang, W., Xu, X., Wang, J.: A neural stochastic volatility model. arXiv preprint arXiv:1712.00504 (2017)
- 17.LeCun, Y., Touresky, D., Hinton, G., Sejnowski, T.: A theoretical framework for back-propagation. In: Proceedings of the 1988 Connectionist Models Summer School (1988)Google Scholar
- 19.Shwartz-Ziv, R., Tishby, N.: Opening the black box of deep neural networks via information. arXiv preprint arXiv:1703.00810 (2017)