We started this chapter by introducing exotic options. In a brief theoretical summary, we explained how exotics and plain vanillas are linked together. There are many types of exotics. We showed one possible way of classification that is consistent with the fExoticOptions package. We showed how the Black-Scholes surface (a 3D chart that contains the price of a derivative dependent on time and the underlying price) can be constructed for any pricing function.

Pricing of exotic options is just the first step. Market makers keep thousands of different options in their trading books. This is possible only because each option can be decomposed into certain sensitivities, the so-called Greeks. Being partial derivatives, Greeks are additive; thus, the portfolio of derivatives has the sum of the Greeks of its elements. The next step was estimating Greeks for any derivative-pricing functions. Our numerical method can be calibrated to the real market conditions; for many parameters, we already...