Risk Latte - Hybrid Conditional Trigger Notes - A product for the bear market

Hybrid Conditional Trigger Notes - A product for the bear market

Team Latte
February 13, 2008

Recently we discussed a product with one of our clients, which is a variation on the classic conditional trigger swaps but in a note form. It is a hybrid structure on S&P500 and USD short term interest rate. The product is a note designed for the bear market and is also a correlation play. Below is a stylized explanation of the note with dummy variables.

The underlying is S&P500 index and the semi-annual coupon payments to the investor are linked to the 6 m USD Libor. There are two barriers, the first barrier, and the second barrier, . Both barriers are set above the current spot level, though the first barrier is very close to the current spot (it can also be at the money). As long as S&P500 stock index is below the first barrier the investor gets a relatively large coupon, say 6 m USD Libor + 125 bp; but if the index goes above the first barrier then the quantum of coupon payment decreases and the it becomes 6m USD Libor + 25 bp.

The structure, however, knock out if the index ever breaches the second barrier on the upside. If S&P500 touches the structure knocks out and all coupon payments cease. On the knock out date the coupon payment is still made, but subsequent coupon payments will cease. The knock out is monitored discretely only on the coupon payment dates. Of course, continuous monitoring of the barrier can also be introduces with daily monitoring and in that case if the structure knocks out on any date other than the coupon payment date, then only one coupon payment will be made, on the date immediately following the knock out date and all other subsequent coupon payments will cease.

The term sheet can be designed with a 2 year maturity or a 5 year maturity. Clearly the longer the maturity of the note, the two barriers have to be adjusted further apart from each other, given the investor's market expectation.

Term Sheet

Underlying : S&P500 Index
Maturity : 5 years
Coupon payment : Semi-annual
First Barrier : 1,400
Second Barrier : 1,800
Coupons :
4.5% for the first semi-annual payment (t = 0.5)
After six months and for all subsequent semi-annual payment
6 m USD Libor + 125 bp if S&P500 is equal to or less than First Barrier
6m USD Libor + 25 bp if S&P500 is greater than First Barrier
Knock Out : the structure knocks out if S&P500 is greater than the Second Barrier

In the above note the investor has a bearish expectation (perhaps a long term bearish expectation) and is benefited with large coupons if the S&P500 index stays below the first barrier.

The above structure can be easily priced using a Monte Carlo framework. Given the knock out barriers one needs to generate stochastic interest rate paths as well besides of course, generating the stochastic equity index paths. The choice of a model for the USD Libor interest rate is material to the pricing and we think that a multi-factor BGM (Libor Market Model) is best suited for this purpose. Modelling the equity index path in a stochastic framework is fairly straightforward.

It is an interesting equity interest rate hybrid structure especially with two barriers, one for deciding on the coupon payment and the other for the knock out level. This gives a lot of flexibility to the note depending what kind of expectations the investor has. Though it is a correlation play from a pricing point of view the impact of correlation between the index and the interest rate on the local volatility of the index can be a challenging exercise to monitor*.

*The idea is inspired from the swap structure given in Equity Derivatives by Marcus Overhaus, et al

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