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Activity Number:
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328
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
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Sponsor:
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Business & Economics Statistics Section
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| Abstract - #301140 |
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Title:
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Long-term Forecasting Based on the Mean Reverting Process with Arbitrarily Distributed Increments
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Author(s):
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Vladimir S. Ladyzhets*+ and Faye Albert and Vladimir Cherepanov
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Companies:
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Hart Re/Yale University and Albert Associates and Domino Bank
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Address:
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38 Kinne Rd., Glastonbury, CT, 06033-3814,
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Keywords:
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mean reverting stochastic process ; long-term forecast ; interest rate options ; Fourier transform
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Abstract:
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A discrete time mean reverting stochastic process with identically and independently distributed increments is considered. No assumptions about the distribution of increments are made: it can be any analytical or empirical distribution. It has been shown that for any given distribution of increments, an N-step ahead forecast for the process can be calculated by applying a recurrent sequence of N one-dimensional Fourier transforms. It has also been proven that for any given distribution of increments the process converges to the asymptotic, time independent, distribution. An efficient method for the calculation of this asymptotic distribution has been developed. It has been demonstrated that in addition to be a "good" approximation to the long-term process development, the asymptotic distribution can be effectively used to obtain the N-step forecast without the laborious recurrent calculations. The practical significance of these results has been illustrated by forecasting payoffs from the long-term interest rate options (LEAPS, traded on the Chicago Board of Option Exchange) that are out-of-the-money at the moment when the forecast is made.
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