Black-Scholes Option Pricing Model in OCaml

bs.ml

let list_sum ls = List.fold_left (fun a x->a+.x) 0.0 ls
let list_init c f = Array.to_list (Array.init c (fun x->f x))

let normal zz = 
  match zz with
  |v when v = 0.0 -> 0.5
  |v when v >= 6.0 -> 1.0
  |v when v <= -6.0 -> 0.0
  |v -> 
    let p = 0.2316419 in
    let b = [0.31938153;-0.356563782;1.781477937;-1.821255978;1.330274428] in
    let f = 1.0/.(sqrt (2.0*.3.1415926)) in
    let abszz = abs_float v in
    let ff = f*.(exp((-.(abszz**2.0)/.2.0))) in
    let sfunc e b = b/.((1.0+.p*.abszz)**e) in
    let sfunclist = list_init 6 (fun x->(sfunc (float x))) in
    let s = list_init 5 (fun x->List.nth sfunclist (x+1) (List.nth b x)) in
    let sz = ff *. (list_sum s) in
    if v>0.0 then 1.0-.sz else sz
  
let blackscholes strike asset standarddev riskfreerate days2expiration =
  let daysinyear = 365.0 in
  let sqrtt days = sqrt (days/.daysinyear) in
  let n strike ass sd r days =
    let ls = log ass in
    let lx = log strike in
    let t = days/.daysinyear in
    let sd2 = sd**2.0 in
    ls-.lx+.r*.t+.(sd2*.t/.2.0) in
  let delta strike ass sd r days = 
    let n = n strike ass sd r days in
    let sqT = sqrtt days in
    let d = sd*.sqT in
    let d1 = n/.d in
    normal d1 in
  let delta2 n sd days =
    let sqT = sqrtt days in
    let d = sd*.sqT in
    let d1 = n/.d in
    normal d1 in
  let nd2 n sd days =
    let sqT = sqrtt days in
    let d = sd*.sqT in
    let d1 = n/.d in
    let d2 = d1-.sd*.sqT in
    normal d2 in
  let bond strike ass sd r days = 
    let n = n strike ass sd r days in
    let t = days/.daysinyear in
    let nd1 = delta2 n sd days in
    let nd2 = nd2 n sd days in
    -.strike*.nd2*.(exp ((-.r)*.t)) in
  let callValue strike ass sd r days =
    let n = n strike ass sd r days in
    let t = days/.daysinyear in
    let nd1 = delta2 n sd days in
    let nd2 = nd2 n sd days in
    let b = bond strike ass sd r days in
    ass*.nd1+.b in
  let putValue strike ass sd r days = 
    let t = days/.daysinyear in
    let call = callValue strike ass sd r days in
    (exp ((-.r)*.t)) *. strike -. ass +. call in
  [(putValue strike asset standarddev riskfreerate days2expiration);
    (callValue strike asset standarddev riskfreerate days2expiration);
    (delta strike asset standarddev riskfreerate days2expiration);
    (bond strike asset standarddev riskfreerate days2expiration)]