Fixed Income Analytics: Duration, Convexity, and Credit

Module: Fintech AI | Difficulty: Advanced

Duration

Convexity

Price Change

Credit Spread

import numpy as np

class BondAnalytics:
    def __init__(self, cashflows, times, yield_to_maturity):
        self.cfs = cashflows; self.times = times; self.ytm = yield_to_maturity
    def price(self):
        return sum(cf / (1+self.ytm)**t for cf, t in zip(self.cfs, self.times))
    def duration(self):
        p = self.price()
        macaulay = sum(t * cf / (1+self.ytm)**t for cf, t in zip(self.cfs, self.times)) / p
        modified = macaulay / (1 + self.ytm)
        return modified
    def convexity(self):
        p = self.price()
        return sum(t * (t+1) * cf / (1+self.ytm)**t for cf, t in zip(self.cfs, self.times)) / (p * (1+self.ytm)**2)

Research Insight: Duration and convexity are fundamental for fixed income risk management. Duration measures interest rate sensitivity, while convexity captures the curvature. For large rate moves, convexity is crucial — high convexity bonds outperform in both rate declines and increases.