bsopt.py 文件源码

def OneTouch( IsHigh, IsDelayed, Spot, Strike, Vol, Texp, Rd, Rf ):
    '''Prices a one touch option. IsHigh=True means it knocks up and in; False
    means down and in. IsDelayed=True means it pays at the end; False means it
    pays on hit.'''

    if ( IsHigh and Spot >= Strike ) or ( not IsHigh and Spot <= Strike ):
        if IsDelayed:
            return exp( -Rd * Texp )
        else:
            return 1

    if Vol <= 0 or Texp <= 0: return 0

    Alpha = log( Strike / float( Spot ) )
    Mu    = Rd - Rf - Vol * Vol / 2.

    if IsDelayed:
        if IsHigh:
            Price = exp( -Rd * Texp ) * ( cnorm( ( -Alpha + Mu * Texp ) / Vol / sqrt( Texp ) ) \
                  + exp( 2 * Mu * Alpha / Vol / Vol ) * cnorm( ( -Alpha - Mu * Texp ) / Vol / sqrt( Texp ) ) )
        else:
            Price = exp( -Rd * Texp ) * ( cnorm( (  Alpha - Mu * Texp ) / Vol / sqrt( Texp ) ) \
                  + exp( 2 * Mu * Alpha / Vol / Vol ) * cnorm( (  Alpha + Mu * Texp ) / Vol / sqrt( Texp ) ) )
    else:
        MuHat = sqrt( Mu * Mu + 2 * Rd * Vol * Vol )
        if IsHigh:
            Price = exp( Alpha / Vol / Vol * ( Mu - MuHat ) ) * cnorm( ( -Alpha + MuHat * Texp ) / Vol / sqrt( Texp ) ) \
                  + exp( Alpha / Vol / Vol * ( Mu + MuHat ) ) * cnorm( ( -Alpha - MuHat * Texp ) / Vol / sqrt( Texp ) )
        else:
            Price = exp( Alpha / Vol / Vol * ( Mu + MuHat ) ) * cnorm( (  Alpha + MuHat * Texp ) / Vol / sqrt( Texp ) ) \
                  + exp( Alpha / Vol / Vol * ( Mu - MuHat ) ) * cnorm( (  Alpha - MuHat * Texp ) / Vol / sqrt( Texp ) )

    return Price