34.4 THE GREEKS

The Greeks are measures that represent the sensitivities of convertible bonds in relation to a variety of factors. These measures got their name because the parameters are often denoted by Greek letters.

34.4.1 Delta and Modified Delta

Delta measures the sensitivity of the value of a derivative security (e.g., a convertible bond) to changes in its underlying asset (i.e., its stock price or parity level). Mathematically, it is the first-order partial derivative of the convertible bond value with respect to the underlying stock price. (Note that the following expression is strictly correct if the conversion ratio is 1. More precisely, delta measures the sensitivity of the bond to changes in its parity value.)

Since the underlying asset of a convertible bond is the stock price times the conversion ratio, the delta of a convertible is calculated using the sensitivity to parity. When using a binomial tree, the delta is also easily obtained by comparing the changes of the convertible value to the changes in parity in the next two nodes. For instance, if the trees in Exhibits 34.6 and 34.9 are used, the delta of the initial node is determined as follows:

This means that a one-point movement in the convertible's parity level will generate a 0.672-point movement in the convertible ...

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