Algorithm to value a path-independent American put option in the binomial model. Up-factor u=2, down-factor d=1/u, s=4 and expiry is at time N, such that the risk neutral probabilities p=q=1/2. The function g determines the intrinsic value (value if exercises immediately). By changing the function g one can value different kinds of American opti…

OptionValue.scala

object OptionValue {
  val N = 2
  val u: Double = 2
  val d: Double = 1/u

  def main(args: Array[String]): Unit = {
    println(v(0,4,(s: Double) => 0.0 max (4.0-s)))
  }
  
  def v(n: Double, s: Double, g: Double => Double): Double =
    if (n == N)
      g(s)
    else
      g(s) max (0.4*(v(n+1, u*s, g) + v(n+1, d*s, g)))
}

PerpetualPut.scala

object PerpetualPut {
  def main(args: Array[String]): Unit = {
    val j = 1
    val s = 2^j
    
    def v(s: Double): Double =
      if (s <=2)
        4-s
      else
        4/s
    
    println(v(8))
  }
}