module QuantLib.Math.Copulas
( Copula (..),
Copulas (..)
) where
class Copula a where
copula :: a -> Double -> Double -> Maybe Double
copula t = precheckRange (copulaFunc t)
copulaFunc :: a -> Double -> Double -> Maybe Double
precheckRange :: (Double->Double->Maybe Double) -> Double -> Double -> Maybe Double
precheckRange f x y
| x >= 0.0 || x <= 1.0
|| y>= 0.0 || y <= 1.0
= f x y
| otherwise
= Nothing
data Copulas = ClaytonCopula Double
| MinCopula
| MaxCopula
| AliMikhailHaqCopula Double
| FarlieGumbelMorgensternCopula Double
| FrankCopula Double
| GalambosCopula Double
| GaussianCopula Double
| GumbelCopula Double
| HuslerReissCopula Double
| IndependentCopula
| MarshallOlkinCopula Double Double
| PlackettCopula Double
instance Copula Copulas where
copulaFunc (ClaytonCopula theta) = claytonCopula theta
copulaFunc MinCopula = minCopula
copulaFunc MaxCopula = maxCopula
copulaFunc (AliMikhailHaqCopula theta) = aliMikhailHaqCopula theta
copulaFunc (FarlieGumbelMorgensternCopula theta) = farlieGumbelMorgenstern theta
copulaFunc (FrankCopula theta) = frankCopula theta
copulaFunc (GalambosCopula theta) = galambosCopula theta
copulaFunc (GaussianCopula rho) = gaussianCopula rho
copulaFunc (GumbelCopula theta) = gumbelCopula theta
copulaFunc (HuslerReissCopula theta) = huslerReissCopula theta
copulaFunc IndependentCopula = independentCopula
copulaFunc (MarshallOlkinCopula a b) = marshallOlkinCopula a b
copulaFunc (PlackettCopula theta) = plackettCopula theta
{-# ANN aliMikhailHaqCopula "NoHerbie" #-}
aliMikhailHaqCopula :: (Fractional a, Ord a) => a -> a -> a -> Maybe a
aliMikhailHaqCopula theta x y
| theta >= -1.0 && theta <= 1.0
= Just ((x*y)/(1.0 - theta * (1.0-x)*(1.0-y)))
| otherwise
= Nothing
{-# ANN farlieGumbelMorgenstern "NoHerbie" #-}
farlieGumbelMorgenstern :: (Fractional a, Ord a) => a -> a -> a -> Maybe a
farlieGumbelMorgenstern theta x y
| theta >= -1.0 && theta <= 1.0
= Just (x*y + theta*x*y*(1.0-x)*(1.0-y))
| otherwise
= Nothing
{-# ANN claytonCopula "NoHerbie" #-}
claytonCopula :: Double -> Double -> Double -> Maybe Double
claytonCopula theta x y
| theta ==0
|| theta < -1.0
= Nothing
| otherwise
= Just $ max( (x ** (-theta) ) + (y ** (-theta)-1.0) ** (-1.0/theta)) 0
minCopula :: Ord a => a -> a -> Maybe a
minCopula x y = Just (min x y)
maxCopula :: (Fractional a, Ord a) => a -> a -> Maybe a
maxCopula x y = Just (max 0.0 (x+y-1.0))
frankCopula :: (Eq a, Floating a) => a -> a -> a -> Maybe a
frankCopula theta x y
| theta == 0.0 = Nothing
| otherwise = Just (-1.0/theta * log (1 + (exp (-theta*x) - 1.0) * (exp (-theta*y) -1.0) / (exp (-theta) - 1.0) ))
{-# ANN galambosCopula "NoHerbie" #-}
galambosCopula :: (Floating a, Ord a) => a -> a -> a -> Maybe a
galambosCopula theta x y
| theta <= 0.0 = Nothing
| otherwise = Just (x * y * exp ( ( (-log x) ** (-theta) + (-log y) ** (-theta) ) ** (-1.0/theta) ))
gaussianCopula :: (Fractional a, Ord a) => a -> t -> t1 -> Maybe a1
gaussianCopula rho _ _
| rho >= -1.0 && rho <= 1.0 = undefined
| otherwise = Nothing
{-# ANN gumbelCopula "NoHerbie" #-}
gumbelCopula :: (Floating a, Ord a) => a -> a -> a -> Maybe a
gumbelCopula theta x y
| theta >= 1.0 = Just (exp ( - ( (-log x) ** theta + (-log y) ** theta) ** (1.0/theta)))
| otherwise = Nothing
huslerReissCopula :: (Fractional a, Ord a) => a -> a -> a -> Maybe a
huslerReissCopula theta _ _
| theta > 0.0 = undefined
| otherwise = Nothing
independentCopula :: Num a => a -> a -> Maybe a
independentCopula x y = Just (x*y)
marshallOlkinCopula :: (Floating a, Ord a) => a -> a -> a -> a -> Maybe a
marshallOlkinCopula a b x y
| a >= 0.0 && b >= 0.0 = Just (min (y * (x ** (1-a))) (x * (y ** (1-b))))
| otherwise = Nothing
{-# ANN plackettCopula "NoHerbie" #-}
plackettCopula :: (Floating a, Ord a) => a -> a -> a -> Maybe a
plackettCopula theta x y
| theta >= 0.0 && theta /= 1.0 = Just $ (sumXyTheta1 - sqrt (sumXyTheta1 * sumXyTheta1 - 4.0 * x * y * theta * theta1))/(2*theta1)
| otherwise = Nothing
where sumXy = x + y
theta1 = theta - 1.0
sumXyTheta1 = 1.0 + theta1 * sumXy