In this chapter we show how to approximate the value of European call options to make the Black Scholes formula easier to evaluate. We do this for at-the-money, near-the-money, and deep out-of-the-money options. Our traditional Taylor Series tool is well used. We also demonstrate a newer “asymptotic series” approach for the deep out-of-the-money options.
In Chapter 23 we solved the Black Scholes equation for a Call Option to yield:
and where N(x) denotes the standard cumulative normal distribution.
This is a fairly complicated formula, although of course it is easy to code it into ...