# Tag Info

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### Derivation of VIX Formula

The piece you are missing is an approximation via the Taylor formula of the logarithm: $$\ln(1+x) \approx x-\frac{x^2}{2} \; .$$ Apply this to the first term in the final formula of the technical ...
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### Why is a variance swap long skew?

As I've mentioned in a comment, it would be wrong to think that entering a variance swap specifically amounts to being "long skew". What you can say however is that, in the absence of jumps (i.e. in ...
• 14.7k
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### Is the VIX more similar to a volatility swap or a variance swap?

The price/value of the VIX index is more akin to the strike/price of a variance swap expressed in vol units than to the strike/price of a vol swap. However, if you are to trade a VIX future (i.e. a ...
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### Why is a variance swap long skew?

If you take Quantuple's stuff a little further, you can really see whether you're long skew. You can pretty easily see the dependence on convexity too (though it should be obvious that you're long ...
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### What are the significant implications of the long-run average variance rate and why Engle won the Nobel Prize for ARCH model development?

The best answer to your question is probably given by the Nobel prize committee itself in "The Prize in Economic Sciences 2003 - Advanced Information" document. You should read it in full. Below is an ...
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### What is the difference between squared returns and variance?

Usually the formula for the sample variance of a stock is given by: $$Var(R_{i}) = E (R_t - E(R_t))^2$$ If you are using daily data to compute the variance then the ...
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### CAPM model as a regression

If you really believed the CAPM's prediction that $\alpha=0$, then imposing $\alpha=0$ in your estimation would indeed lead to your 2nd formula. The problems? The CAPM doesn't work so imposing a ...
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### Heston: Variance of Integrated Variance

Studying zero-coupon bond prices in the CIR (1985) short rate model, $\text{d}r_t=\kappa(\theta-r_t)\text{d}t+\xi\sqrt{r_t}\text{d}W_t$, Hirsa (2013, Section 1.2.6.2) states that the characteristic ...
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### Static and Dynamic Hedging of Vol/Var Swaps

There has been a lot of work in recent years on the pricing and hedging of volatility derivatives, leading to some non-obvious, even startling results. It is summarized in Mark Joshi's book More ...
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### Intuition Behind Scaling Factor in Variance Swaps

I believe you want to know why the VIX is a weighted portfolio of calls and puts with weights proportional to $\frac{1}{K^2}$ (NB: obviously the T is there to adjust for time to maturity, hence is not ...
• 1,896