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

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.