module Quant.VolSurf ( VolSurf (..) , FlatSurf (..) ) where import Quant.YieldCurve {- | The 'VolSurf' class defines the basic operations of a volatility surface. Minimal complete definition: 'vol'. -} class VolSurf a where -- | Calculate the implied vol for a given strike/maturity. vol :: VolSurf a => a -> Double -> Double -> Double -- | Calculate the variance at a given strike/maturity. var :: VolSurf a => a -> Double -> Double -> Double var vs s t = v*v*t where v = vol vs s t -- | Calculates Dupire local vol for a given strike/maturity/forward generating yield curve. localVol :: (VolSurf a, YieldCurve b) => a -- ^ Volatility surface -> Double -- ^ Initial stock price -> b -- ^ 'YieldCurve' to generate forwards -> Double -- ^ Current stock level -> Double -- ^ Time -> Double -- ^ Local volatility localVol v s0 rcurve k t | w==0.0 || solution<0.0 = sqrt dwdt | otherwise = sqrt solution where dr = disc rcurve t f = s0/dr y = log $ k/f dy = 1.0E-6 [kp, km] = [k*exp dy, k/exp dy] [w, wp, wm] = map (\x->var v (x/s0) t) [k, kp, km] dwdy = (wp-wm)/2.0/dy d2wdy2 = (wp-2.0*w+wm)/dy/dy dt = min 0.0001 (t/2.0) dwdt = let strikept = k*dr/drpt strikemt = k*dr/drmt drpt = disc rcurve $ t+dt drmt = disc rcurve $ t-dt in case t of 0 -> (var v (strikept/s0) (t+dt) -w)/dt _ -> (var v (strikept/s0) (t+dt)-var v (strikemt/s0) (t-dt))/2.0/dt solution = dwdt/(1.0-y/w*dwdy+0.25*(-0.25-1.0/w+y*y/w/w)*dwdy*dwdy+0.5*d2wdy2) -- |A flat surface has one volatility at all times/maturities. data FlatSurf = FlatSurf Double instance VolSurf FlatSurf where vol (FlatSurf x) _ _ = x