Bond duration, convexity and return

_.py

def modified_duration(y, m):
    """
    Approximates the modified duration of a risk-free bond at par value.

    :param y: Yield-to-maturity in decimal terms
    :param m: Maturity in years
    :return: Modified duration of a risk-free bond
    """
    return (1-(1/(1+0.5*y)**(2*m)))/(y)

def convexity(y, m):
    """
    Approximates the convexity of a par bond.
    
    :param y: Yield-to-maturity in decimal terms
    :param m: Remaining maturity in years
    :return: The convexity of a bond
    """
    return (2/(y**2))*(1-(1/(1+0.5*y)**(2*m)))-(2*m)/((y)*(1+0.5*y)**(2*m+1))

def bond_return(y, m, prev_y, mod_dur, convexity, months=1):
    """
    Calculates the return on a bond.
    
    :param y: Current yield (t)
    :param m: Maturity in years
    :param prev_y: Previous yield (t-1)
    :param mod_dur: Modified duration
    :param convexity: Convexity of bond
    :param months: Number of months between current yield and previous yield, default is 1
    :return: Return on bond
    """
    return -mod_dur*(y-prev_y)+0.5*convexity*(y-prev_y)**2+((1+prev_y)**(months/12)-1)