Back in 1973, Fischer Black and Myron Scholes published a paper, "The Pricing of Options and Corporate Liabilities”, where they derived a differential equation to try to model the value of some kinds of options, initially only European type. The term “Black and Scholes” was coined by Robert C. Merton in a further study that developed the mathematical model behind.
Nowadays, it is the most used equation in high level finance, after, of course, of the Time Value of Money equation.
Now, all financial HP calculators, and most HP graphical calculators in my memory, have the TVM equation. Even the children who use the Prime have access to calculate their own mortgage - not a good learning for a youngster!
But the Black and Scholes formula has not found its way to HP calculators until the HP30b. This is, as far as I know, the only calculator made with the Black and Scholes formula built in.
But, of course, being the HP calculators the gold standard in finance, it was clear that there would be ports of the formula to most calculators. The HP12c, that I still see in all financial boardrooms that I visit, is very limited with its 99 program steps; but I have found at least three programs for it - all of them using most of the memory.
By its nature, the best calculator to handle the Black and Scholes formula is the HP17bII with its integrated solver. You can find an example of B&S formula in -of all places- HP’s very own website. To save you some search time, I enclose the formula. Just seeing it, I don’t have any willingness to enter it! Won’t work first time, sure; and debugging it will take a lot of time.
Tomorrow we will see other approaches to solve it, with more/less precision and occupying more or less memory, and for other calculator models