A Class of Gaussian Hybrid Processes for Modeling Financial Markets |
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Authors: | Yasuyuki Itoh |
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Institution: | (1) Power and Industrial Systems Research and Development Center, Toshiba Corporation, 1, Toshiba-cho, Fuchu-Shi, Tokyo 183-8511, Japan |
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Abstract: | This paper proposes a one-factor model of financial markets using a class of Gaussian process that can be decomposed into
a Brownian motion and an Ornstein–Uhlenbeck process. It is shown that this “hybrid” process is obtained as a continuous-time
scaling limit of the differenced first-order autoregressive integrated moving average (ARIMA(1,1,1)) process. Parameter estimations
using an ARIMA(1,1,1) framework and its variance ratio test show the accuracy of the proposed model. Construction of the one-factor
commodity futures price model is presented as an application. A multidimensional extension of the hybrid process is also presented
in the Appendix. |
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Keywords: | Ornstein– Uhlenbeck process Brownian motion Non-stationary Gaussian process ARIMA Variance ratio test Commodity price Term structure of futures price |
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