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...