2-Factor Black Non-smiled Montecarlo

[katsuwaka]

Create montecarlo model with 2 x underlyings

Assumption

• 2 x Black underlyings with continuous dividends (eg FX, index)
• Volatility as function of time, no smie
• Correlation between -1 and +1
• Both underlying quoted on same currency unit

Input

• Spot : S1, S2
• Risk-free rate : rate(t)
• Dividend yield: div1(t), div2(t)
• Repo yield: repo1(t), repo2(t)
• Volatility : vol1(t), vol2(t)
• Correlation : rho or rho(t)
• Cash flow: Map[t:Double, f:(Double, Double) => Double]

Required function

• price(cashflow):Map[Double, Double]
  where result is mapping payment date => price

Example

val r = t => 0.01 + 0.002 * t
val rho = 0.75

val S1 = 100.0
val div1 = t => 0.03 + 0.003 * t
val repo1 = t => 0.0
val vol1 = t => 0.25 + 0.01 * t

val S2 = 150.0
val div2 = t => 0.05 + 0.003 * t
val repo2 = t => 0.0
val vol2 = t => 0.20 + 0.01 * t

val cashflow = Map[
0.5 -> (x:Double, y:Double) => math.max(0.0, math.min(x - 100.0, y - 150.0)),
1.0 -> (x:Double, y:Double) => math.max(0.0, math.min(x - 100.0, y - 150.0)),
1.5 -> (x:Double, y:Double) => math.max(0.0, math.min(x - 100.0, y - 150.0)),
2.0 -> (x:Double, y:Double) => math.max(0.0, math.min(x - 100.0, y - 150.0)),
]

price(cashflow) = Map[
0.5 -> 4.225, 
1.0 -> 4.10, 
1.5 -> 3.85, 
2.0 -> 3.555, 
] (or something like this, numbers are complete random)