Plotting convexity vs. the factor
Another way to check what effect a certain factor has on bond convexity is to directly plot a graph of this factor against the bond's convexity.
In this exercise, you will price a 20 year bond with a 6% coupon and face value of USD 100, then find the convexity of this bond for different levels of yields.
numpy, numpy_financial, pandas, and matplotlib have already been imported for you as np, npf, pd, and plt, respectively.
This exercise is part of the course
Bond Valuation and Analysis in Python
Exercise instructions
- Create an array of bond yields from 0 to 20 in increments of 0.1 and convert to a
pandasDataFrame. - Find the price of the bond, shift the yields up and down and reprice, then calculate the convexity of the bond.
- Plot a graph of bond yields on the x-axis against convexity on the y-axis.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Create array of bond yields and covert to pandas DataFrame
bond_yields = np.arange(____, ____, ____)
bond = pd.DataFrame(____, columns=['bond_yield'])
# Find price of bond, reprice for higher and lower yields, calculate convexity
bond['price'] = -npf.pv(rate=bond['____'] / 100, nper=____, pmt=____, fv=____)
bond['price_up'] = ____
bond['price_down'] = ____
bond['convexity'] = (bond['____'] + bond['____'] - 2 * bond['____']) / (bond['____'] * 0.01 ** 2)
# Create plot of bond yields against convexity, add labels to axes, display plot
plt.plot(bond['____'], bond['____'])
plt.xlabel('Yield (%)')
plt.ylabel('Convexity')
____