Installment Call Warrants on Hang Seng Index
April 24, 2008
Note: This product idea is straightforward adaptation of the installment warrants on TSE-35 index issued by Bankers Trust Canada in 1994*.
There is a lot of interest in the Hang Seng Index (HSI), despite the recent precipitous fall in the index over the last couple of months. A large number of investors in Hong Kong and elsewhere in North Asia - including both the retail as well as institutional investors - believe that this is really not a bear market and that the fall was a correction from where the equity markets, and the HSI, will rally much higher. The main issue in the minds of such investors is the timing.
One type of structured product that may suit such investors could be an installment warrant. A bank can issue an installment call warrant on the Hang Seng Index such that the investor pays 40% of the premium upfront, and he has the option to pay the balance 60% at a later date in case he is proven right on the direction of the market.
Say, a bank issues a call warrant on Hang Seng Index with a maturity of two years and the premium of the warrant (warrant price) is HK$8.00. The investor would be required to pay only say, 40% of this premium, i.e. HK$3.20, today (upfront upon buying the warrant) and the balance of the 60% would be payable after one year and that too at the discretion of the investor. In other words, after one year from today, the investor may choose to invest another 50% (HK$4.80) and receive an American style call option on Hang Seng Index. Or he may choose not to invest the balance of the 60% and let the warrant (the first option) expire worthless.
The strike price of the warrant could be 100. This is essentially a compound call option. It is a European style call option with one year maturity on an American style call option with one year maturity on the Hang Seng Index.
The product payoff could like something like this:
||Installment Call Warrant
||Hang Seng Index
||Call option on Hang Seng Index
|First Option Type
|Second Option Type
||May 1, 2008
|Maturity of Warrant
||2 years (May 1, 2010)
|Maturity of Call Option
||1 year (May 1, 2009)
As explained by Izzy Nelken, it may not be possible to use Rubinstein's Newton-Rahpson method for compound options to this product because the structure is a European option whose underlying is an American call option.
The product can however be done in a straightforward way using Numerical Integration routine (as explained elsewhere in this site). Numerical quadrature is a robust method and an adaptive routine for such is Q1DA by Kahaner, Moler and Nash**. This method is explained in detail in Compound Options and Chooser Options by Izzy Nelken in Exotic Options***.
The value of this compound call option is given by the numerical integral:
In the above the limits of the integral will be transformed to finite numbers.
K1 is the first strike price (that of the European call option) and
K2 is the second strike price (that of the American call option). S is the underlying and T is the maturity of the warrant. T - t
is the time when the investor decides whether to pay the second installment and receive the American call on the index.
*Reference: Exotic Options - Instruments, Analysis and Applications, edited by Israel Nelken (Irwin Professional Publishing).
** Kahaner, D., C. Moler, and S. Nash, Numerical Methods and Software (Prentice Hall Series in Computational Mathematics, 1989).
***Exotic Options (see above).
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