Haug (2007a) comprehensively covers the collection of pricing formulas for around 100 exotic derivatives. The fOptions and fExoticOptions packages are based on this book. Wilmott (2006), Taleb (1997), and DeRosa (2011) describe a lot of practical issues about them.

The first impression could be that there are way too many exotic options. There are many ways of classification. Market makers talk about different generations of exotics, such as first generation, second generation, and so on. Their approach is from a hedging point of view. We will use a slightly different angle, the end-user approach, and classify the options based on their main exotic feature.

Asian type exotics are about the average. It could be an average rate or an average strike, and it could also be an arithmetic or geometric average. These options are path dependent; that is, their value at expiry is not purely a function of the underlying price at expiry but the total path. Asian options are cheaper...