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A New Approach for Computing Option Prices of the Hull-White Type with Stepwise Reversion and Volatility Functions

Hui Jin, Jun-Ya Gotoh and Ushio Sumita
The Journal of Derivatives Fall 2007, 15 (1) 67-85; DOI: https://doi.org/10.3905/jod.2007.694793
Hui Jin
An assistant professor at School of Finance and Economics, Hangzhou Dianzi University in Hangzhou, China.
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  • For correspondence: jinhui@hdu.edu.cn
Jun-Ya Gotoh
An associate professor at Department of Industrial and Systems Engineering, Chuo University in Tokyo, Japan.
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  • For correspondence: jgoto@indsys.chuo-u.ac.jp
Ushio Sumita
A professor at Graduate School of Systems and Information Engineering, University of Tsukuba in Tsukuba, Japan.
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  • For correspondence: sumita@sk.tsukuba.ac.jp
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Abstract

Interest rate models, starting with Vasicek, generally include mean-reversion toward a long term level. As such models were applied in the real world to price interest-dependent instruments, including derivatives, they were extended in order to match observed market prices. One way is to introduce more stochastic factors, but the other is to introduce mean-reversion and other kinds of nonstochastic time variation for important parameters, notably volatility. Incorporating such flexibility into a single stochastic factor interest rate lattice requires some method of discretizing these functions, and it is not always easy. In this article, Jin, Gotoh and Sumita develop a new technique involving the use of Ehrenfest functions to approximate mean-reverting O-U processes. Performance of their approach is comparable to a trinomial tree, but it has the advantage of being operational for parameter values for which a trinomial breaks down. It may also facilitate pricing of more complex instruments, with barriers and other such features.

TOPICS: Derivatives, statistical methods, technical analysis

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The Journal of Derivatives
Vol. 15, Issue 1
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A New Approach for Computing Option Prices of the Hull-White Type with Stepwise Reversion and Volatility Functions
Hui Jin, Jun-Ya Gotoh, Ushio Sumita
The Journal of Derivatives Aug 2007, 15 (1) 67-85; DOI: 10.3905/jod.2007.694793

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A New Approach for Computing Option Prices of the Hull-White Type with Stepwise Reversion and Volatility Functions
Hui Jin, Jun-Ya Gotoh, Ushio Sumita
The Journal of Derivatives Aug 2007, 15 (1) 67-85; DOI: 10.3905/jod.2007.694793
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