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.
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:
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 ...