Constructing a Volatility Smile in Excel
Constructing a volatility smile using the Malz smile model builds understanding of the volatility surface market instruments. The Black-Scholes framework can then be used to calculate strikes for different deltas to show how the market instruments impact strike placement within the volatility smile.
Task A: Set Up the Malz Smile Model
Recall the Malz formula for implied volatility at a given (positive) delta put from Chapter 12:
This formula can be coded up in Excel:
Check that and the 25% put delta and 25% call delta (75% put delta) implied volatility matches up with the standard approximations:
Task B: Plot Implied Volatility versus Delta and Investigate Parameters
The function output can be extended to generate a full volatility smile from 0% to 100% delta:
The volatility smile can then be plotted:
Check that the volatility ...