// object binomial extends App { 
  import scala.math._

   type BinomialTree = Array[Array[Double]]

   def makeTree(T: Int): BinomialTree = {
      val B: BinomialTree = new Array(1+T)
      for (t <- 0 to T) B(t) = new Array(1+t)
      B
   }

   def constVol(c0: Double, T: Int, U: Double, D: Double) = {
      val C = makeTree(T)
      C(0)(0) = c0
      for (t <- 1 to T) {
        C(t)(0) = C(t - 1)(0) * D
        for (u <- 1 to t) C(t)(u) = C(t - 1)(u - 1) * U
      }
      C
    }

   def backRecurse(C: BinomialTree, tAgg: (Double, Double) => Double, CE: (Double, Double) => Double) = {
      val T = C.length - 1
      val V = makeTree(T)
      for (u <- 0 to T) V(T)(u) = C(T)(u)
      for (t <- T - 1 to 0 by -1)
        for (u <- 0 to t)
          V(t)(u) = tAgg(CE(V(t + 1)(u + 1), V(t + 1)(u)), C(t)(u))
      V
    }

  def siCE(p: Double, cRRA: Double, uV: Double, dV: Double) = {
    val power = 1 - cRRA // assume cRRA away from one
    pow(p * pow(uV, power) + (1-p) * pow(dV, power), 1 / power)
  }

  val alphaValues = List(2.0, 20.0, 40.0)
  val beta = 0.03
  val gamma = 2.0
  val delta = 1.0 / 1.5
  val muHi = 0.05
  val muLo = 0.00
  val sigma = 0.03
  val nPeriods = 560
  val horizon = 10.0
  val h = horizon / nPeriods
  val pHi = (1 + (muHi / sigma) * sqrt(h)) / 2.0
  val pLo = (1 + (muLo / sigma) * sqrt(h)) / 2.0
  val upGrowth = exp(sigma * sqrt(h))
  val dnGrowth = 1 / upGrowth
  val C = constVol(100, nPeriods, upGrowth, dnGrowth)
  val discount = exp(-beta * h)
  val tAgg = siCE(discount, delta, _: Double, _: Double)
  val hiCE = siCE(pHi, gamma, _: Double, _: Double)
  val loCE = siCE(pLo, gamma, _: Double, _: Double)

  for (alpha <- alphaValues) {
    val U = backRecurse(C, tAgg, (x, y) => siCE(0.5, alpha, hiCE(x, y), loCE(x, y)))
    println("For alpha = " + alpha + " the time-zero utility is " + U(0)(0))
  }

// }