Target redemption notes Example 7.5% USD Target Redemption Index Linked Deposit (issued by Bank of East Asia, 2004) Selling points - Enjoy potentially higher returns with Index Linked Deposit 100% principal protection plus 7.5% guaranteed coupon return over a maximum of 5-year investment period. 1 st year annual coupon is guaranteed at 6.5% (very juicy), payable semi-annually. The remaining coupon rate of 1% will be based on the LIBOR movement. The inverse floater formula is max{7% 2 6-month LIBOR (in arrears), 0} However, the total coupon received will not shoot beyond the target rate of 7.5%. If the coupon payment accrued during the deposit period is less than the target rate, then the remaining amount will be paid at maturity.
Early termination Once the accumulated coupon payment reached the target rate, the deposit will be terminated automatically. Worst scenario The deposit is held for 5 years until maturity so that the annual return for the deposit is only 1.5% per annum. Market background The US Fed policy makers voted unanimously to keep the Fed Fund Rate unchanged at 1% on 28 October 2003, the lowest level in the past 45 years. They had indicated that the interest rate would remain at a low level for a considerable period. Potential risk If the 6-month LIBOR rises beyond 3.5% one year afterwards and never come down again. The deposit is then held for 5 years until maturity.
Valuation approach The note value is given by the sum of present value of all potential future cashflows. Since the termination date is uncertain, the cashflow on the coupon date t k, k = 1, 2,..., K, is stochastic. N L(r, t k ; τ) Pt T A k c k c cap notional amount τ-period LIBOR at time t k (with dependence on interest rates) value of unit-par discount bond at time t with maturity date T accumulated coupon amount up to coupon date t k coupon payment received at t k target coupon cap rate
Inverse floater formula N τ max{f ml(r, t k ; τ), 0} Running sum of coupon received A k = N τ k j=1 max{f ml(r, t k ; τ, 0}, A k Nc cap. Coupon payment received at t k c k = min(max(nc cap A k 1, 0), N τ max{f ml(r, t k ; τ, 0}) Define a stopping time t k of hitting the target rate, the index k is a positive integer satisfying 1 k K such that k = sup{k A k 1 < Nc cap }. Implicitly, we have c k = 0 when k k K. The pricing model resembles an Asian barrier option, where the knock-out feature depends on the path dependence variable A (running accumulated coupon sum).
Discounted cash flows received by the note holder Y = Ne t k t r(u) du + [ e t K t ] r(u) du max(nc cap A K, 0) + K k=1 c k e t k t r(u) du Note that e t k t r(u) du is the discount factor over the period [t, t k ]. The first term represents the par payment at the knock-out date t k. When k = K, the note survives until maturity. The last term represents the sum of cash flows received at all coupon dates and maturity date t K. The second term represents the payoff of a European put option at t K with dependence on the stochastic quantity A K. When the accumulated coupon payments have not reached the target cap rate at maturity, the remaining amount of the target coupon is paid out (in additional to the par) at maturity.
Modeling of the interest rate uncertainty Interest rate effect enters as (i) discount factor (ii) calculation of coupon payment (dependence on the LIBOR rate) One factor short rate model would imply full correlation of all future LIBOR rates. However, the use of a short rate model with more factors would make numerical valuation cumbersome. In reality, interest rate fluctuations occur by jump, say, decision made by the US Federal Reserve Board. The simple diffusion models cannot capture such effect.
Equity target redemption notes SG Product 10-year fund that is 100% capital guaranteed Pay a juicy fixed coupon of 10% in the first year For Year Two, the coupon payment is referenced to the average performance of the 6 worst stocks in a basket of 24 blue-chip stocks. max{0, 10% + 0.5 average performance of the 6 worst stocks} From Year Three onwards, the investor gets the better of the previous year s coupon or the payout formula. Once the aggregate coupon payments reaches or exceeds 20%, the fund terminates with full payment of the coupon for that year. Worst scenario: 10-year fund with total coupon of 20%
Blending equity and rates Design products that have both equity and fixed-income risk. The equity and fixed-income markets typically offset each other during economic downturns, therefore hedging the investor against excessive downside in one market. Examples 1. A note that automatically switches between a bond and equity index once the initial index reaches a certain barrier. 2. Combination of an equity range accrual and a LIBOR range accrual, with the coupon dependent on the number of days in an observation period where both indexes are within the range.