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Valuation of callable accreting interest rate swaps: Least squares Monte-Carlo method under Hull-White interest rate model

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  • Tang, Kin-Boon
  • Zheng, Wen-Jie
  • Lin, Chao-Yang
  • Lin, Shih-Kuei

Abstract

Using the Hull-White interest rate model, this paper proposes a valuation method of callable accreting interest rate swap (CAIRS) and how it can be used for managing the risk of zero callable bonds (ZCBs). Firstly, CAIRS can be decomposed into accreting payer interest rate swaps and Bermudan options. Considering the financial valuation of both components, the former can be valued directly while the latter has no close-form due to its early exercise characteristics. Using the Least Squares Monte-Carlo method (LSM) proposed by Longstaff and Schwartz (2001), we find that the two options embedded in ZCB and CAIRS have the same exercise strategy since the terms of the swaps will include the bonds in practice. However, the cash flow of risk management in swaps and bonds can differ when considering the time value. Hence, CAIRS is not the best financial instrument for managing risks of ZCB under the current design.

Suggested Citation

  • Tang, Kin-Boon & Zheng, Wen-Jie & Lin, Chao-Yang & Lin, Shih-Kuei, 2021. "Valuation of callable accreting interest rate swaps: Least squares Monte-Carlo method under Hull-White interest rate model," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    • Handle: RePEc:eee:ecofin:v:56:y:2021:i:c:s1062940820302242
    DOI: 10.1016/j.najef.2020.101339
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    3. Ball, Clifford A. & Torous, Walter N., 1983. "Bond Price Dynamics and Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(4), pages 517-531, December.
    4. Peter A. Abken, 1991. "Beyond plain vanilla: a taxonomy of swaps," Economic Review, Federal Reserve Bank of Atlanta, issue Mar, pages 12-29.
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. Brennan, M J & Schwartz, Eduardo S, 1977. "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion," Journal of Finance, American Finance Association, vol. 32(5), pages 1699-1715, December.
    7. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
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