It seems there was a misunderstanding. I am aware of the approach of using weekly options to estimate the implied volatility structure, akin to creating a synthetic VIX-like indicator. By utilizing the prices of weekly options, one can derive a snapshot of market expectations of volatility over the short term, potentially without the need for constant rebalancing, thus saving on transaction costs. However, my concern was about ensuring the no-arbitrage condition while employing this method.Using cubic spline interpolation on the implied volatilities derived from these weekly options can indeed provide a smooth curve across different strike prices. Yet, it's crucial that this method adheres to the no-arbitrage condition to prevent any mispricing or incorrect risk assessments. Any methodology that overlooks the no-arbitrage condition could lead to misleading conclusions about the volatility structure, regardless of the data source, be it prices of options or the underlying security.The no-arbitrage condition is fundamental for maintaining a reliable and robust model, ensuring consistency and validity in the financial markets. So, while the approach of using weekly options combined with cubic spline interpolation might offer a way to estimate implied volatility, it's essential to confirm that this method satisfies the no-arbitrage condition to provide a truly accurate representation of the implied volatility structure.