Black-Scholes Option Pricing Model in F#

black-scholes.fs

let normal zz =
  let p = 0.2316419
  let b = [0.31938153;-0.356563782;1.781477937;-1.821255978;1.330274428]
  let f = 1.0/(sqrt (2.0*3.1415926))
  let abszz = abs zz
  let ff = f*(exp((-(abszz**2.0)/2.0)))
  let sfunc e b = b/((1.0+p*abszz)**e)
  let sfunclist = List.init 6 (fun x->(sfunc (float x)))
  let s = List.init 5 (fun x->List.nth sfunclist (x+1) (List.nth b x))
  let sz = ff * (List.sum s)
  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 when v < 0.0 -> sz
  |v -> 1.0 - sz

let blackscholes strike asset standarddev riskfreerate days2expiration =
  let daysinyear = 365.0
  let sqrtt days = sqrt (days/daysinyear)
  let n strike s sd r days =
    let ls = log s
    let lx = log strike
    let t = days/daysinyear
    let sd2 = sd**2.0
    ls-lx+r*t+(sd2*t/2.0)
  let delta strike s sd r days = 
    let n = n strike s sd r days
    let sqT = sqrtt days
    let d = sd*sqT
    let d1 = n/d
    normal d1
  let delta2 n sd days =
    let sqT = sqrtt days
    let d = sd*sqT
    let d1 = n/d
    normal d1
  let nd2 n sd days =
    let sqT = sqrtt days
    let d = sd*sqT
    let d1 = n/d
    let d2 = d1-sd*sqT
    normal d2
  let bond strike s sd r days = 
    let n = n strike s sd r days
    let t = days/daysinyear
    let nd1 = delta2 n sd days
    let nd2 = nd2 n sd days
    -strike*nd2*(exp (-r*t))
  let callValue strike s sd r days =
    let n = n strike s sd r days
    let t = days/daysinyear
    let nd1 = delta2 n sd days
    let nd2 = nd2 n sd days
    let b = bond strike s sd r days
    s*nd1+b
  let putValue strike s sd r days = 
    let t = days/daysinyear
    let call = callValue strike s sd r days
    (exp (-r*t)) * strike - s + call
  [putValue strike asset standarddev riskfreerate days2expiration;
    callValue strike asset standarddev riskfreerate days2expiration;
    delta strike asset standarddev riskfreerate days2expiration;
    bond strike asset standarddev riskfreerate days2expiration]