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Variance Premia; disentangled. Let me address this question a bit differently and bring the question forward: What part (i.e. 'side') of the volatility smile attracts a significant premium in relationship to the underlying uncertainty that it is trading? To this end, let us define the physical, i.e. empirical (average realized) return semivariance as: $$ SV_\...


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I think you are mixing up a few things. As @noob2 pointed out, there is a negative correlation between price changes and IVOL changes (what explains this is not 100% clear in the literature - however, a simple explanation is that markets fall much more quickly than they rise). The largest positive daily percent changes in S&P500 were all in times of ...


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I really like that question and hope someone else also provides additional answers or insights. MOVE measures the implied yield volatility. TYVIX measured price vol (less commonly used - so I guess flawed construction). The Price of Fixed Income Market Volatility may be interesting to read. The author(s) are directly involved in the creation of some of these ...


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Simply make sure the forward variances remain non negative: $\Sigma(T_{i+1})^2 T_{i+1} - \Sigma(T_{i})^2 T_{i} \geq 0$ for all $i$.


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The VIX, has a concave shape for its option's Implied volatility.


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If quick and simple works, the formula by Malz is quite easy to implement. If you have access to an automated data import tool, I suspect you use one of the common vendors. In this case it may be worth to ask if they have an API that pulls you the exact value based on a request for say 35DC with expiry in x days. E.g. Bloomberg would allow you to pull single ...


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I doubt anyone will provide or have a vol surface for this. Well, if it is sold, your market maker will price that but that is a different story in my opinion. It's like buying insurance for your car vs a Bugatti Chiron. The latter will not follow standard logic and likely have a hefty premium to a "theoretical" price of insurance. Long term vol ...


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I do not think there is any problem. Firstly, you also did not use OIS but LIBOR now, although the "appropriate" risk free rate would be OIS. You also did not compare the two. To address the risk that one or more IBORs are discontinued while market participants continue to have exposure to that rate, counterparties are encouraged to agree to ...


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Risk.net: Calling out autocallable pricing offers an intuitive explanation of modelling issues with autocallables with baskets. Since the vast majority of AC are based on baskets, this is very relevant. LV is simply insufficient. I like this tweet, it's funny and accurate at the same time. The same guy has a rant that explains issues with AC pricing quite ...


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Very old but seems to miss an answer. If $$K=fe^{-\frac12\sigma^2\tau}$$ is your appropriate formula, you use premium adjusted delta, and get the ATM delta neutral strike. Makes sense for EURPLN which should be Delta premium included by convention. In this case, you have a bigger issue than forward prices. There is no closed form solution and you need a root ...


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Frequently, American options are de-Americanized. Afterward, you "simply" use the standard model you use to construct your VOL surface based on European prices. In reality, things are quite messy though: You need data filtering to ensure the reliability of the inputs (do you use several exchanges vs most liquid, stale prices, unreliable bid-ask ...


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Generally, FINCAD is correct. I do have some reservations though. Yes, variance swaps have a theoretical replication. A vanilla option trader following a delta-hedging strategy is essentially replicating the payoff of a weighted variance swap where the daily squared returns are weighted by the option’s dollar gamma. Taking this argument one step further, a ...


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"Warrant Arbitrage", the attempt to take advantage of warrants mispricing in volatility terms was one of the first applications of the Black Scholes theory decades ago. I don't know where things stand today, but I doubt that there are large volatility discrepancies today (although as pointed out in other answer warrants are not very liquid so it ...


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Table 3 shows the math needed to get Delta neutral strikes. P.a. stands for premium adjusted which is also explained in the paper. It is a very good paper to read. Equity VOL surfaces are fundamentally different. Generally, derived from listed option prices (with all complexities involved in that). FX is relatively simple. ATM Delta neutral Straddles (DNS), ...


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"And why don't other banks exploit too expensive warrants by buying them from their peers and hedge the position at the EUREX?" If the warrants are expensive relative to options, the way to exploit them is to sell them and buy the cheaper options as a hedge, not to buy the warrants. And that is the reason why they cannot be exploited in the way you ...


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This depends on the currency you're looking at really. If you are pricing a cap/floor on for example EUR or CHF, then using Black is not particularly useful. The reason is because you have both negative strikes (e.g. -50bp floor) and negative rates which results in a big hole in the volatility surface. You will notice that up to ~10 years time to expiry that ...


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True, but you use LV at the money very "locally". If your K>S0 or K<S0, for your first step you will use LV(new K = S0,0) which considered at the money localy but not in global since S0!=K(at the end). It s very tricky and it s how the process of LV is defined.


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