Greeks

Understanding the risk-types that an option might involve is crucial for all market participants. The idea behind Greeks is to measure the different types of risks; they represent the sensitivity of the option to different factors. The Greeks of a plain vanilla option are: delta (, sensitivity to the underlying price), gamma (, sensitivity of delta to the underlying price, delta of delta), theta (, sensitivity to time), rho (, sensitivity to the risk-free rate), and vega (V, sensitivity to the volatility). In terms of mathematics, all Greeks are partial derivatives of the derivative price:

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The Greeks can be computed easily for each option with the GBSGreeks function:

> sapply(c('delta', 'gamma', 'vega', 'theta', 'rho'), function(greek)
+   GBSGreeks(Selection = greek, TypeFlag = "c", S = 900, X = 950,
+     Time = 1/4, r = 0.02, b = 0.02, sigma = 0.22)
+ )
    delta         gamma          vega         theta           rho
0.347874404   0.003733069 166.308230868 -79.001505841  72...