The Uncarved Block

I have been interested in functional programming for some time, but finally decided to bite the bullet and learn properly, and that (for me anyway) means writing some code to accomplish a practical task. My idea is to reimplement most of the C++ code in Mark Joshi's excellent book C++ Design Patterns and Derivatives Pricing, but in OCaml. Now I'm a newcomer to functional programming and to ocaml, so what I write won't be pretty or idiomatic, especially at first. To begin with I'm learning from the main tutorial. If I find and use another I'll post that too.

I will try to explain some of the financial stuff that's going on as I do so, but for the full lowdown on why derivatives price the way they do, you need to learn some financial maths. You could do a lot worse that picking up Joshi's other book, The Concepts and Practice of Mathematical Finance. A lot of people get Hull, but I prefer Joshi for a really practical introduction with great explanations of concepts. When I was at Goldman, a lot of people were very sarcastic about Hull as a source. I don't really have a credible opinion about that.

So without further ado, here is my first ocaml program, which defines payoffs for vanilla European put and call options. In fact Joshi starts off straight away with a Monte Carlo pricer, but my copy is downstairs so I'm straying off-piste here. It's my intention to follow Joshi step by step, and write up each one here as I go.

open Printf

(* a vanilla option pays off the difference between the spot price
 * and the strike, or expires worthless *)
let put_payoff strike spot=
        max ( strike -. spot ) 0.0;;

let call_payoff strike spot=
        max (spot -. strike ) 0.0;;

let print_payoff payoff strike spot=
        let outcome=payoff strike spot in
        printf "%f\n" outcome;;

print_payoff call_payoff 195.0 190.0;;
print_payoff call_payoff 195.0 200.0;;
print_payoff put_payoff 195.0 190.0;;
print_payoff put_payoff 190.0 195.0;;

Now I'm running and writing this on fedora Linux, and my ocaml is 3.09.3. When I run this I see:

% ocaml tmp/payoff.ml
5.000000
0.000000
0.000000
5.000000

Which is what I would expect. Now this is very cheesy at present, but it's a start and we'll improve it in the next article. It's worth a couple of observations about this because already this demonstrates a few things that strike me as being interesting about ocaml. For one thing, there isn't any default type promotion or operator overloading, so we need to explicitly qualify our constants with .0 to get them to be floats. Secondly, we need to use -. to subtract them. The max function can operate on any type so it works with floats or ints.