FX Correlation Products - Best/Worst of Options, Dual Digitals, FX Quantos, Basket Options

Something about correlation
There's something about correlation which investors don't like. It's difficult to manage. For one thing, it is invisible. Market data on implied correlation(expected future correlation) is rare, and even if available, its reliability is in doubt. The time when you really need a correlation hedge to work, it may work against you. It's difficult to predict how correlation will behave in an aftermath of a crisis. It tends to rise towards 1 in times of crisis  and breakdown as market normalises.

Comparison of 3mth implied volatilities on FX majors compiled by JP Morgan vs S&P VIX index during the 2008 Lehman crisis and during the European sovereign debt crisis in May 2010.
Source: Bloomberg

 That said, managing correlation risk is easier in the forex world compared to other asset classes due to the breadth and depth and transparency of the underlying options markets.
Forex volatility as a macro hedge is also relatively cheaper and it's not uncommon for portfolio managers to trade forex to hedge cross asset portfolios even though there's a mismatch of risk between the hedge and the underlying. Recall correlation between asset classes shot up during a crisis. So even if forex is only 70% correlated with the asset class you are trying to hedge, some hedge is still better than none.
Here's a brief intro on some of the products which correlation plays a crucial role in their characteristics and pricing. A thing to note: As implied correlation is not a directly observable market data, it's common to derive correlation via implied volatilies. For a 2 ccy pairs basket, the risk can be classified under the leading pairs and their cross. Implied correl is derived using the implied vols of the 3 ccy pairs (2 leading pairs + their cross) via the well-known finance equation: Vol(3)*Vol(3) = Vol(1)*Vol(1) + Vol(2)*Vol(2) + 2*correl*Vol(1)*Vol(2). Data on implied vols are more readily available and reliable than correl data.

Best/Worst of Option
Payout is based on the best/worst of performing pair on a basket of currencies.
For a 2 ccy basket, best-of-option payout = max {(S1-X1),(S2-X2),0}
                               worst-of-option payout = min {(S1-X1),(S2-X2),0}
Intuitively, best-of-option tends to be expensive. It costs more than a single pair vanilla option but less than the sum of underlying constituents in the basket. For worst-of-options, they cost less than a single pair vanila option. Low correlation for best-of-option is pricier compared to a high correlation basket. In fact, it is better if correlation is negative as there's a greater likelihood that the underlyings would move in opposite direction and you would still get a payout based on the best return. The reverse is true for worst-of-option basket (pricier if correl is high). A worst-of-option basket on 2 ccy pairs costs  about half of the price of a single ccy option.
Worst-of-option has been very popular recently. During the EUR sovereign crisis, implied vols on USD/EUR shot up to a hefty premium. It's expensive to buy USD/EUR vanilla. Worst of EUR puts against a basket of ccy offered a cheaper hedge and similar payout if the view on a broad base depreciation of EUR proved correct. This is not an outlandish assumption if the EUR crisis were to blow up.

Dual Digital
This is another popular product recently. For a european dual digital, the buyer receives  a fixed rebate if the 2 ccy pairs move above or below a target level at expiry. If the payout is possible only if the 2 pairs move above the target level, premium would be substantially lower than the single pair digital if correl is negative. This is because the negative correl means there's a higher probability of the 2 pairs moving in opposite direction and hence not paying out at expiry.

FX basket
Return is based on performance of the underlyings in the basket. Due to correl being <1 for the underliers, a basket has lower volatility and so a basket option is cheaper.

FX Quanto
This is an investment product with payout in a different currency from the original ccy. To illustrate, a SG  investor buys a USD put/JPY call digital. Payout is in JPY if USD/JPY is below 80 at expiry. The investor will have to convert the JPY proceeds to SGD at the prevailing fx rate and will benefit from from a positive correl  between USD/JPY and  SGD/JPY. In a quanto, SGD/JPY risk is eliminated as the JPY payout is converted to SGD at a fixed rate. Thus it costs the investor less to buy a quanto on USD put/JPY call digital compared to normal digital if correl is positive.
Quantos between FX and other asset classes are common and allow foreign investment without FX risk.