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For VIX and VVIX you can try FirstRate Data which has 1-minute bars going back 5 years


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Okay, here my only opinion and it's not the academic answer that you should rely on, just "on-desk experience", but anyway. Answering your question about: Have you ever seen these returns calculated like this? According to CDS. - definitely not. If we are talking about single-name CDS derivative instrument. (not about index one). I double @Dimitri's answer ...


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I'll try my best to explain them Both of them aim to match the implied volatility surface as shown by the empirical data. Local volatility process is a function of Stock and time without any stochastic term (not moving randomly). It changes with with different inputs of stock and time. It matches the implied volatility surface with short term maturity ...


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The skew/smile of long term options is flatter than short term options, the reason for this can be explained in several ways. The Vega of a shorter-dated option is smaller than a longer-dated option. Vega is the dollar value of a 1% change in implied volatility. i.e., 30d ATM option, $65 strike, .31 ivol = VEGA .07 30d 25 delta option,31% ivol = ...


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The volatilities of short dated options are more sensitive to market changes as compared to those of long dated options. This is implied by square root of time rule. As such, volatility skew are larger for short dated options.


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One possible reason could be jumps. Over the longer maturity, there could be more jumps so the jumps average out in a way; whereas over the short term, a jump can make a bigger difference and hence the risk of jump increases demand. This reasoning is used to justify Stochastic volatility with jumps models in some books.


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