Frequently Asked Questions In Quantitative Finance

Chapter 2: FAQs 137

whereV(S,t) is the option value as a function of stock

price,S,andtime,t. Of course, there may be other inde-

pendent variables. The limiting procedure in the above

is the clue to how to approximate such derivatives

based on continuous variables by differences based

on discrete variables.

The first step in the finite-difference methods is to lay

down a grid, such as the one shown in Figure 2-7.

The grid typically has equally spaced asset points, and

equally spaced time steps. Although in more sophis-

S

k t

i

V

i

k

Figure 2-7:The finite-difference grid.