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 ...

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