The Greeks for free
In the binomial tree pricing models that we have covered so far, we traversed up and down the tree at each point in time to determine the node values. From the information at each node, we can reuse these computed values easily. One such use is the computation of Greeks.
The Greeks measures the sensitivities of the price of derivatives such as options with respect to changes in parameters of its underlying asset, often represented by Greek letters. In mathematical finance, the common names associated with Greeks include: alpha, beta, delta, gamma, vega, theta, and rho.
Two particularly useful Greeks for options are delta and gamma. Delta measures the sensitivity of the option price with respect to the underlying asset price. Gamma measures the rate of change in delta with respect to the underlying price.
As shown in the following figure, an additional layer of nodes is added around our original two-step tree to make it a four-step tree, which extends two steps backward...
