Forecasting Financial Processes by Using Diffusion Models
DOI:
https://doi.org/10.12775/DEM.2010.005Keywords
diffusion models, ex-post forecasts, Monte-Carlo simulation, the GARCH model, the ARIMA model, unit-rootAbstract
Time series forecasting is one of the most important issues in the financial econometrics. In the face of growing interest in models with continuous time, as well as rapid development of methods of their estimation, we try to use the diffusion models to modeling and forecasting time series from various financial markets. We use Monte-Carlo-based method, introduced by Cziraky and Kucherenko (2008). Received forecasts are confronted with those determined with the commonly applied parametrical time series models.
References
Black, F., Scholes, M. (1973), The Pricing of Option and Corporate Liabilities, Journal of Political Economy, 81, 637–659. DOI: http://dx.doi.org/10.1086/260062
Broadie, M., Jain, A. (2008), Pricing and Hedging Volatility Derivatives, Journal of Derivatives, 15, Issue 3, 7–24. DOI: http://dx.doi.org/10.3905/jod.2008.702503
Chan, K. C., Karolyi, G. A., Longstaff, F. A., Sanders, A. B. (1992), An Empirical Comparison of Alternative Models of Short Term Interest Rates, Journal of Finance, 47, 1209–1227. DOI: http://dx.doi.org/10.2307/2328983
Cliff, M. T. (2003) GMM and MINZ Program Libraries for Matlab, Krannert Graduate School of Management Purdue University.
Cox, J. C., Ingersoll, J., Ross, S. (1985), A Theory of the Term Structure of Interest Rates, Econometrica, 53, 385–407. DOI: http://dx.doi.org/10.2307/1911242
Cziraky, D., Kucherenko, S. (2008), Monte Carlo Forecasting from CIR Square Root Diffusion Models, BRODA Ltd. http://www.broda.co.uk (8.01.2009).
Detemple, J., Osakwe, S. (1999), The Valuation of Volatility Options, CIRANO Paper, Scientific Series.
Doman, M., Doman, R. (2004), Econometric Modeling of Polish Financial Market Dynamic (In Polish), Poznań University of Economics, Poznań.
Engle, R. F. (1982), Autoregressive Conditional Heteroscedacticity with Estimates of the Variance of United Kingsdom Inflation, Econometrica, 50, 987–1007.
Hansen, L. P. (1982), Large Sample Properties of Generalized Method Of Moments Estimators, Econometrica, 50, 1029–1054. DOI: http://dx.doi.org/10.2307/1912775
Heston, S. L. (1993), A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, The Review of Financial Studies, 6, Issue 2, 327–343. DOI: http://dx.doi.org/10.1093/rfs/6.2.327
Howison, S., Rafailidis, A., Rasmussen, H. (2004), On the Pricing and Hedging of Volatility Derivatives, Applied Mathematical Finance, 11, Issue 2, 317–346. DOI: http://dx.doi.org/10.1080/1350486042000254024
Javaheri, A., Wilmott, P., Haug, E. (2002), GARCH and Volatility Swaps, Wilmott Magazine, January, 1–17.
Jagannathan R., Kaplin A., Sun S. G. (2004), An Evaluation of Multi-Factor CIR Models Using Libor, Swap Rates, and Cap and Swaption Prices, Journal of Econometrics, 116, 113–146.
Ljung, G. M., Box, G. E. P. (1978), On a Measure of Lack of fit in Time Series Models, Biometrika, 65, 297–303. DOI: http://dx.doi.org/10.2307/2335207
Mannolini, A., Mari, C., Renò, R. (2008), Pricing Caps and Floors with the Extended CIR Model, International Journal of Finance & Economics, 13 (4) 386–400. DOI: http://dx.doi.org/10.1002/ijfe.369
McLeod, A. I., Li, W. K. (1983), Diagnostic Checking ARMA Time Series Models Using Squared Residual Autocorrelations, Journal of Time Series Analysis, 4, 269–273. DOI: http://dx.doi.org/10.1111/j.1467-9892.1983.tb00373.x
Merton, R. C. (1973), Theory of Rational Option Pricing, Bell Journal of Economics and Management Science, 4 (1) 141–183. DOI: http://dx.doi.org/10.2307/3003143
Merton, R. C. (1974), On The Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, 449–470. DOI: http://dx.doi.org/10.2307/2978814
Nelson, D. (1991), Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59, 347–370. DOI: http://dx.doi.org/10.2307/2938260
Newey, W. K., West, K. D. (1987), A Simple, Positive Semidefinite, Heteroskedasticity and Autocorrelation Consistant Covariance Matrix, Economerica, 59, 347–370.
Phillips, P. C. B., Perron, P. (1988), Testing for a Unit Root in Time Series Regressions, Biometrika, 75, 335–346. DOI: http://dx.doi.org/10.2307/2336182
Phillips, P. C. B., Yu, J. (2009), A Two-Stage Realized Volatility Approach to Estimation of Diffusion Processes with Discrete Data, Journal of Econometrics, 150, Issue 2, 139–150.
Psychoyios, D., Skiadopoulos, G. (2006), Volatility Options: Hedging Effectiveness, Pricing, and Model Error, Journal of Futures Markets, 26, 1–31. DOI: http://dx.doi.org/10.1002/fut.20181
Said, E., Dickey, D.A. (1984), Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order, Biometrika, 71, 599–607. DOI: http://dx.doi.org/10.2307/2336570
Sepp, A. (2008), VIX Option Pricing in a Jump-Diffusion Model, Risk, April, 84–89.
Vašiček, O. (1977), An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5, 177–188.
Tamba, Y. (2006), Pricing the Bermudan Swaption with the Efficient Calibration, NUCB Journal of Economics and Information Science, 51, Issue 1, 17–31.
Welfe, A. (1998), Econometrics (In Polish), Polskie Wydawnictwo Ekonomiczne, Warszawa.
Yoshida, N. (1992), Estimation for Diffusion Processes From Discrete Observation, Journal of Multivariate Analysis, 41, 220–242. DOI: http://dx.doi.org/10.1016/0047-259X(92)90068-Q
Downloads
Published
How to Cite
Issue
Section
License
The journal provides an Open Access to its content based on the non-exclusive licence Creative Commons (CC BY-ND 4.0).
To enable the publisher to disseminate the author's work to the fullest extent, the author must agrees to the terms and conditions of the License Agreement with Nicolaus Copernicus University.
Stats
Number of views and downloads: 418
Number of citations: 0
