# Tag Info

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No, it's not. First, what you ought to be regressing are returns, not prices. Second, by interpolating you're underestimating the variance of the asset price in the interval between index price observations. Through your choice of interpolation method, you're essentially picking an arbitrary price in the middle. What you ought to be doing is maximum ...

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To expand on pbr142, If the implied volatility (vis. Black & Scholes) is persistently higher for short-expiry contracts away from the money, the problem is the model, not the thing that's modeled. The price of a contract at a given point in time is the "correct" price at that point in time (or we should move this to philosophy.stackexchange.com). So ...

2

You have to remember that implied volatility comes from a "wrong" model to give the right answer. Option prices are determined by supply and demand (subject to a few arbitrage bounds). A higher implied volatility for OTM/ITM options relative to ATM options simply means that the prices of these options are higher than the Black-Scholes model would imply ...

0

you never trade spot volatility. you exchange it for something else. if you want to exchange it for spot implied volatility, you buy a volatility swap. if you want to exchange it for forward implied volatility you get options.

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Basis point implied volatility is calculated as follows: $\sigma_{bp} = \frac{100F\sigma}{DV01}$ where $F$ is the price of underlying TY future, $\sigma$ is implied volatility, and $DV01$ is a dollar duration of the cheapest to deliver bond (it is published daily by the exchange, or can be calculated manually). The calculation of $DV01$ using modified ...

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They are not referring to any implied volatility but actual volatility, i.e. statistical standard deviation. The price volatility is the annualized standard deviation of bond price changes and the yield volatility the annualized standard deviation of bond yield changes. These quantities are usually estimated using a historical estimator. If you have n ...

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In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be $$RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t)$$ where RV(t,T) is an estimate of the realized volatility from t to ...

2

Recall that the delta of an option is the sensitivity of its price to changes in the underlying's stock price: $$\Delta = \frac{\partial V}{\partial S}$$ Now, if you assume the BS framework, you find that: $$V(t,T,K,\sigma,r) = S_t \Phi(d_1) - e^{-r(T-t)} K \Phi(d_2)$$ Clearly, $\Delta = \frac{\partial V}{\partial S}= \Phi(d_1)$. Note that $d_1$ is a ...

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Given that by delta means that if the price goes up by 0.01% i.e. one basis point, you gain 15 and vice versa if the price goes down by one basis point. You know that the daily standard deviation is 2.2%, than again you know that $220*15 = 3300$ is the standard deviation of your portfolio. So, since we are using a normal distribution you can look at a table ...

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My understanding is you can calibrate with atm vol which should be close with either model then the otm vols are taken care of by the beta parameter from sabr

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I think what you are missing is simply the Vega-Gamma relation in the Black-Scholes model. Namely: $$Vega = \frac{\partial v}{\partial \sigma} = \sigma(T-t)S^2 \frac{\partial^2 v}{\partial S^2} = \sigma \tau S^2 \Gamma$$ Plugging this into your coverage error, you get its expression in terms of the Vega which is the most natural measurement of your ...

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Perhaps not the most encouraging answer, but: I would think that it is contingent upon the specific implementation, magnitude, regularity, and transiency of arbitrage available as well as the volatility estimate time-scale. In a very simple case, the existence of arbitrage opportunities would likely result in larger fraction of informed traders (relative to ...

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If you look at it from a mathematical point of view - presence of arbitrage should not matter for volatility estimates. Absence of arbitrage can be associated with the existence of an equivalent martingale measure for the bank account numeraire. (first fundamental theorem of asset pricing) Let's assume the real world process is something like ...

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Sure, the variance of the total wealth can be expressed in terms of the variances and covariances of the prices of the assets. If $$W = \sum_{i} \pi_i P_i$$ where $\pi_i$ is the total dollar amount invested in asset $i$ with price $P_i$. The variance of total wealth is then  Var(W) = \sum_i \pi_i Var(P_i) + \sum_i \sum_{j, j\neq i} \pi_i \pi_j Cov(P_i, ...

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