Risk Latte - The Range Box Product

The Range Box Product

Team Latte
Aug 31, 2005

The range box product was quite popular in the mid nineties with FX traders and investors and very recently we came across a trade in Asia which was of this nature.

A large regional bank has bought from its client (supposedly an insurance company) a knock out (KO) call option and a knock out put option for one year on Dollar-Yen. The note is structured such that the KO call and the KO put are bought simultaneously and the strike of the call was 103.00 and that of the put was 117.00. The spot was trading at 109.00 and the KO call was a call on USD and put on JPY and the KO put was a put on USD and call on USD. This is a classic range box product.

The question we asked ourselves was that why would an insurance company (assuming the buyer of the option was indeed an insurance company) want to sell a range box structure to a bank. Of course, there are numerous instances whereby insurance companies sell options to banks in order to make the up-front premium as yield (and a lot of them lose their shirts on these trades). But in this case the structure is a range box structure with a KO call and a KO put and therefore, (a) the premium from selling these KO options is not going to be big and (b) if for some reason the volatility of USD-JPY moves down then the first exit time will be lengthened and hedging these options may prove to be difficult for the insurance company.

The only reason – or at least the main reason – why the bank would want to buy this product would be that it holds the view that Dollar-Yen volatility will trend down and that these options will not be knocked out soon. In fact the bank has to believe that the volatility will go down quite substantially for it to profit from the trade.

Anyway, let’s look at the range box structure. This is a classic range box product whereby the investor buys a knock out call with a strike K1 and a knock out put with a strike K2 on the same underlying. K1 is below the current spot and K2 is above the current spot. If the spot remains within these two ranges then on maturity the buyer of the product gets the payoff from the KO call and a KO put. In fact, this payoff is simply the difference of the two strikes. Therefore, on maturity the buyer of the option gets the difference However, if either of the strikes is hit then both the call and the put are knocked out. The KO call and put are both in the money.

The payoff of the structure is:

The first exit time of this structure is very short and the structure will at best look like a reverse knock out. Under a worst case scenario it would seem that the structure wants to expire immediately. In fact, one of the better ways to understand these structures is to look at American style double bets.

The seller of this product would be betting on the fact that due to extremely short first exit time the options will be knocked out very soon and thereby he can pocket the premium. The buyer of the product would be betting on the fact that the volatility of the underlying – USD/JPY in this example – will go down substantially and he will profit from the options remaining in the money on expiry.

We did a back of the envelope pricing of the above product using Monte Carlo simulation. For 1,000 runs and constant USD/JPY volatility of 11% (USD risk free rate of 3% and spot at 109.00 and lower strike at 103 and the upper strike at 117). The price comes out to be 0.473% of the notional.

Of course, a more detailed pricing with around 100,000 simulation runs and local volatility surface (rather than constant vol) will make the price more realistic and robust.

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