TARGET REDEMPTION NOTES Chi Chiu CHU 1 Yue Kuen KWOK 23 The target redemption note is an index linked note that provides a guaranteed sum of coupons (target cap) with the possibility of early termination. In a typical structure, the coupons are calculated based on an inverse floating LIBOR / Euribor formula. Once the accumulated amount of coupons has reached the pre-specified target cap, the note will be terminated with final payment of the par. The knock-out criterion depends on a path dependent state variable defined by the running accumulated coupon sum. In some simplified cases, we manage to obtain a closed form valuation formula for the note value. We propose several numerical schemes for pricing the note under the one-factor and two-factor short rate models. Pricing behaviors of the target redemption note are also explored. 1 INTROUDCTION A target redemption note is similar to an inverse floating rate note, embedded with additional features like the possibility of early termination and a guaranteed sum of coupon payments. As an example, let us consider the 5-year target redemption note issued by Credit Suisse First Boston on 10 November, 2003. The first year coupon rate is fixed at 9%. The coupon rates in subsequent years are calculated based on an inverse floating formula, max(8.65% − 2L, 0), where the index L denotes the 12-month Euribor on the coupon date. The note will be terminated prematurely on a coupon date when the accumulated coupon rate meets the target cap of 15%. The salient feature of the note is that the date of the par payment is uncertain, which is taken to be the earlier date among the pre-specified note’s maturity date and the coupon date when the accumulated coupon amount meets the target cap. The lure of a handsome initial coupon combined with the perception that the par may be received within a short span of time has made these notes attractive to Asian retail investors in the early 2000’s when the interest rates were at a low level. Obviously, the investor has a higher gain on the time value of the cash flow stream when the Euribor decreases since a shorter time is required to collect the coupon payments and par. At the other extreme, the investor faces the worst scenario when the 12-month Euribor trades above 4.325% one year later and never comes down again. In this case, he then has to hold the note for 5 years and receive the par and the remaining coupon on the maturity date. The note value is given by the sum of present values of the par and coupon payments and this sum depends on the times at which the payments are received by the note holder. The interest rate fluctuation leads to uncertainty in the coupon payments received on the coupon dates, and also results in uncertainty in the redemption date of the note (knock-out). The uncertainty regarding the termination date is governed by a path dependent variable, which is the running accumulated coupon sum. The note 1 Chi Chiu Chu is in the Department of Statistics, University of Toronto, Toronto, Ontario M5S 3G3, Canada 2 Yue Kuen Kwok is in the Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China 3 Correspondence author, Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong; fax number: (852)-2358-1643; e-mail: maykwok@ust.hk. 1 This is the Pre-Published Version