LO 15.8: Explain the im pact o f the volatility smile on the calculation o f the

LO 15.8: Explain the im pact o f the volatility smile on the calculation o f the Greeks.
Option Greeks indicate expected changes in option prices given changes in the underlying factors that affect option prices.
The problem here is that option Greeks, including delta and vega, may be affected by the implied volatility of an option. Remember these guidelines for how implied volatility may affect the Greek calculations of an option:
The first guideline is the sticky strike rule, which makes an assumption that an options
implied volatility is the same over short time periods (e.g., successive days). If this is the case, the Greek calculations of an option are assumed to be unaffected, as long as the implied volatility is unchanged. If implied volatility changes, the option sensitivity calculations may not yield the correct figures.
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Topic 15 Cross Reference to GARP Assigned Reading – Hull, Chapter 20
The second guideline is the sticky delta rule, which assumes the relationship between an
options price and the ratio of underlying to strike price applies in subsequent periods. The idea here is that the implied volatility reflects the moneyness of the option, so the delta calculation includes an adjustment factor for implied volatility. If the sticky delta rule holds, the options delta will be larger than that given by the Black-Scholes-Merton formula.
Keep in mind, however, that both rules assume the volatility smile is flat for all option maturities. If this is not the case, the rules are not internally consistent and, to correct for a non-flat volatility smile, we would have to rely on an implied volatility function or tree to correctly calculate option Greeks.
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