The EWMA and GARCH approaches to volatility clustering are independent of the method used to calculate VaR. Therefore Choice 'd' is the correct answer

The CCAR is a supervisory mechanism adopted by the US Federal Reserve Bank to assess capital adequacy for bank holding companies it supervises. It was not a concept introduced by the international Basel framework.
The other three were indeed rules introduced by Basel 2.5, which was ultimately subsumed into Basel III.
Stressed VaR is just the standard 99%/10 day VaR, calculated with the assumption that relevant market factors are under stress.
The Incremental Risk Charge (IRC) is an estimate of default and migration risk of unsecuritized credit products in the trading book. (Though this may sound like a credit risk term, it relates to market risk - for example, a bond rated A being downgraded to BBB. In the old days, the banking book where loans to customers are held was the primary source of credit risk, but with OTC trading and complex products the trading book also now holds a good deal of credit risk. Both IRC and CRM account for these.) While IRC considers only non-securitized products, the CRM (Comprehensive Risk Model) considers securitized products such as tranches, CDOs, and correlation based instruments.
The IRC, SVaR and CRM complement standard VaR by covering risks that are not included in a standard VaR model. Their results are therefore added to the VaR for capital adequacy determination.

Once the frequency distribution has been determined (for example, using the binomial, Poisson or the negative binomial distributions) and the severity distribution has also been determined (for example, using the lognormal, gamma or other functions), the loss distribution can be produced by a Monte Carlo simulation using successive drawings from each of these two distributions. It is assumed that the severity and frequency are independent of each other. The resulting distribution gives a distribution showing the losses for operational risk, from which there Op Risk VaR can be determined using the appropriate percentile.Therefore Choice 'b' is the correct answer.

According to Basel II, where marking-to-market is not possible, banks may mark-to-model, where this can be demonstrated to be prudent. Marking-to-model is defined as any valuation which has to be benchmarked, extrapolated or otherwise calculated from a market input. When marking to model, an extra degree of conservatism is appropriate. Supervisory authorities will consider thefollowing in assessing whether a mark- to-model valuation is prudent:
* Senior management should be aware of the elements of the trading book which are subject to mark to model and should understand the materiality of the uncertainty this creates in the reporting of the risk/performance of the business.
* Market inputs should be sourced, to the extent possible, in line with market prices. The appropriateness of the market inputs for the particular position being valued should be reviewed regularly.
* Where available, generally accepted valuation methodologies for particular products should be used as far as possible.
* Where the model is developed by the institution itself, it should be based on appropriate assumptions, which have been assessed and challenged by suitably qualified parties independent of the development process. The model should be developed or approved independently of the front office. It should be independently tested.
This includes validating the mathematics, the assumptions and the software implementation.
* There should be formal change control procedures in place and a secure copy of the model should be held and periodically used to check valuations.
* Risk management should be aware of the weaknesses of the models used and how best to reflect those in the valuation output.
* The model should be subject to periodic review to determine the accuracy of its performance (e.g. assessing continued appropriateness of the assumptions, analysis of P&L versus risk factors, comparison of actual close out values to model outputs).
* Valuation adjustments should be made as appropriate, for example, to cover the uncertainty of the model valuation.
The model should be created independent of the front office, and not by it. Therefore statement III does not represent an appropriate choice. Choice 'a' is the correct answer.

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.