As we explained in the introductory part of this chapter, Greeks are partial derivatives. Some important Greeks are as follows:

In some simple cases, these partial derivatives can be found analytically. For example, the fOptions package includes the GBSGreeks function that gives the Greeks for vanillas.

Analytical Greeks are convenient; however, there are two problems with them. The first problem is that market-traded parameters are not changing in infinitesimal small increments. For example, on the New York Stock Exchange, the smallest possible change in the stock price is one cent. The stock price either changes at least one cent or there is no change at all. On the...