Risk Latte - Principal Protected Composite JPY Note

Principal Protected Composite JPY Note

Team Latte
July 30, 2006

A principal protected zero coupon composite JPY note was issued by a European bank to US based institutional investors last year in mid-July in Asia . The note allowed the investors to bet on an up move in both the Nikkei225 index stocks and the Dollar Yen. The payoff of the note was:

We do not have the term sheet of this note and hence we do not know as to what was price at which this note was sold (this was narrated to us by a reliable source). Also, we have modified the payoff and substituted the Nikkei225 index in place of a basket of Japanese stocks which made the note slightly more complex.

The embedded option in the note is a "composite" option, which is distinctly different from a "quanto" option. It is a bit difficult to value a composite option in a closed form because the two options cannot be unbundled (a favourable movement in Nikkei index will be offset by an unfavourable movement in the Dollar-Yen). The option is both a call on the underlying index, which is Nikkei 225 as well as a call on the FX rate which is USD/JPY. But the two call options cannot be separated easily and priced.

The above note was issued to investors who had a 5 year bullish view on both the USD/JPY FX rate as well as the Nikkei225 index (Japanese stocks). One can ask the question: why should the investor buy this note rather than simply buying two call options - one on the Nikkei and the other on the Dollar-Yen? The answer is: in almost all cases, a composite option costs less than the sum of two call options and behaves pretty much in the same way. However, a composite is definitely more expense than a quanto option and the reason is obvious (quantos have reduced upside due to fixed FX rate whereas the composites have greater upside due to a variable FX rate).

The above structure can be easily priced using Monte Carlo simulation technique.

  1. Try to think of a closed form solution for the above option? (Remember that 1/1000 is just a scaling factor).

  2. Given the present level of Dollar-Yen and the Nikkei 225, will an investor who bought the note in July 2005 be in the money or out of the money?

  3. Price the Composite option (preferably using Monte Carlo simulation and then find the price of a 5 year call on Nikkei and a 5 year call on Dollar-Yen, using the above strike and volatility of 17% on Nikkei and 10% on Dollar-Yen and then compare the price of the composite with the sum of the calls.

You can send your answers to team@risklatte.xyz .

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