The Valuation and Hedging of the Path-dependent and Path-independent Range Notes
Date Issued
2004
Date
2004
Author(s)
Lin, Chia-Chin
DOI
zh-TW
Abstract
The main purposes of this paper are to value and to hedge the Path-dependent and Path-independent range notes. The first is to derive exact analytical valuation formulas for target redemption notes and range notes with double barrier of knock-out digital options in the context of a multi-factor Gaussian Heath, Jarrow, and Morton (1992) term structure model. The last is to find the best tools which exists in the derivatives markets and then we can use it to hedge or unwind the products (for example: target redemption notes and range notes with double barrier of knock-out digital options).
A target redemption note pays a floating, inverse floating, or fixed coupon rate at the end of each coupon period, based on the value of some reference interest rate (e.g. 6-month US Libor) in the beginning of each coupon period. However, a range note with double barrier of knock-out digital options, which belongs to a Path-dependent range note, pays a fixed coupon rate at the end of each compounding period, based on the value of the reference interest rate in the compounding period. And unlike a standard range note, the coupon also depends on the number of days that the reference interest rate all lies inside a corridor during each compounding period.
Next sections are organized as follows. Section 2 describes the most relevant probabilistic features of the multi-factor Gaussian HJM model that will be used hereafter. Section 3 introduces the Path-dependent and Path-independent range notes. Section 4 provides closed-form solutions for the exotic options that will be used to price non-standard range notes. Section 5 prices non-standard range notes and generalizes, under a multi-factor formulation. Then, section 6 discusses how to hedge these kinds of products. Finally, section 7 concludes.
Subjects
利率區間債券
路徑相依區間債券
金字塔型債券
Target Redemption Note
Range Note
Type
thesis
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