## Greeks – the link back to the vanilla world

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

**delta**: This denotes the DvalueDspot, which is the change of the option price with respect to the change of the underlying spot price**gamma**: This denotes the DdeltaDspot**vega**: This denotes the DvalueDvolatility**theta**: This denotes the DvalueDtime**rho**: This denotes the DvalueDinterest rate

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...