VSTOXX Demo (Original)¶

Background¶

Implied Volatility Vstoxx Demo

Educational script demonstrating implied volatility vstoxx demo concepts.

Code¶

```python """ Implied Volatility Vstoxx Demo

Educational script demonstrating implied volatility vstoxx demo concepts. """

import numpy as np import matplotlib.pyplot as plt

Requires: ImpliedVol class¶

Data: vstoxx_data_31032014.h5¶

Download from: https://github.com/psygement/financepy/blob/master/part1/ch03/source/vstoxx_data_31032014.h5¶

======================================================================¶

def main(): S = 17.6639 # 2014-03-31 VSTOXX Close # K read from data # T read from data r = 0.01 # sigma will be computed in this code

iv = ImpliedVol(S, r, tol=0.5)
iv.compute_implied_volatility()
# read only rows with implied volatility computed
# if not computed, corresponding 'IMP_VOL' is np.NaN
df = iv.options_data
df.dropna(subset='IMP_VOL',inplace=True)

maturities = sorted(set(df['MATURITY']))

fig, ax = plt.subplots(figsize=(12,5))
for maturity in maturities: # maturity --- Timestamp object, for example Timestamp('2014-04-18 02:00:00')
    data = df[df.MATURITY == maturity] # select data for this maturity
    ax.plot(data['STRIKE'], data['IMP_VOL'], label=maturity.date(), lw=0.7, alpha=0.9, ls="--",
            marker='.',
            markersize=5,
            markeredgecolor='black',
            markeredgewidth=0.1,
            markerfacecolor='black')
ax.grid()
ax.set_xlabel('strike')
ax.set_ylabel('implied volatility')
ax.legend()
plt.show()

if name == "main": main() ```

Exercises¶

Exercise 1. The VSTOXX close on 2014-03-31 was 17.6639. Explain what this number represents and its units.

Exercise 2. The IV smiles are plotted for multiple maturities. Explain why shorter maturities typically show steeper smiles than longer maturities.

Exercise 3. Options with IV marked as NaN failed the computation. List three common reasons for IV computation failure.

Exercise 4. From the smile plot, estimate the 25-delta put and 25-delta call IVs for the nearest maturity. Compute the risk reversal and butterfly spread.