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The Shift Function for the Extended Vasicek Model

In: Advances In Quantitative Analysis Of Finance And Accounting

Author

Listed:
  • Shyan Yuan Lee

    (National Taiwan University, Taiwan, R.O.C.)

  • Hsi Hsieh Cheng

    (National Taipei College of Business, Taiwan, R.O.C.)

Abstract

This study has two main purposes. The paper first derives the shift function and bond price formulas for the Hull-White extended Vasicek model, which simultaneously fits current yield curve and volatility curve. The result of Kijima and Nagayama (1994) is extended by allowing the instantaneous standard deviation of the short rate to be time-dependent, which permits the closed-form formulas for the shift function and bond price to be derived. By applying these formulas, the shift function and the bond price at each node can be obtained without calculation on a tree. Some numerical examples are given to demonstrate the effectiveness of these formulas. The second purpose of this study is to discuss how to estimate the “unobservable” time-dependent standard deviation of the short rate from the “observable” spot rate volatility curve. The theoretical relation between the time-dependent standard deviation of the short rate and the volatility curve of the spot rate is derived. This paper demonstrates this relation for two different functional forms of the time-dependent standard deviation of the short rate, and also shows how to estimate the time-dependent standard deviation via this relation.

Suggested Citation

  • Shyan Yuan Lee & Hsi Hsieh Cheng, 2006. "The Shift Function for the Extended Vasicek Model," World Scientific Book Chapters, in: Cheng-Few Lee (ed.), Advances In Quantitative Analysis Of Finance And Accounting, chapter 11, pages 255-270, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812772824_0011
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