The index option is affected by the spot value for the underlying index, as also the risk free interest rate, or the zero rate for the duration of the option. It is also affected by the volatility of the underlying. The 'strike price' is set and is fixed at the time the option is purchased, and therefore is not a risk factor.
Therefore other than IV, all other choices are valid risk factors that underlie an equity index option.
Other instruments may have other risk factors - for example, a long forex position will have the spot exchange rate as the only risk factor.
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