6

The well-known formula expressing the price of a variance swap as a function of an (infinite) strip of European options is actually not that model-free: it assumes that the price process follows a pure diffusion, i.e. that it does not jump. So my two cents would be: Even if you could trade an infinite strip of options you would only be able to replicate the ...


4

The (undiscounted) value of any derivative is the expected value of the payoff. So the (undiscounted) value of a varswawp is: $$\mathbb{E}\left[ \mathrm{Notional} \cdot 10000 \cdot \left( K^2 - \frac{252}{N} \sum_{i=1}^N \left(\ln \frac{S_i}{S_{i-1}} \right)^2\right) \right]$$ Where, we can move everything that's static outside of the expectation, and ...


4

For Variance Swaps (and Vol swaps with some caveats), the Black Scholes model is the main tool used for pricing. It is just less obvious. Using your example, options are not priced with S-K or K-S either. That is simply an algebraic expression of parts of the contract. Pricing involves finding a value for this. There is no assumption on pricing configuration ...


3

In this month's Risk magazine, there was a research paper stating precisely There is no liquidity in the variance swaps of interest rates.


1

I think the $^+$ was just a typo. Nice question! I'll try to make this point in the case of interest-rates, but the argument is general. To some extent it’s case by case, but the general feature of a swap is to be fair - that is, worth $0$ - at inception, say $t=0$. This can be achieved setting to an appropriate value the fixed rate/vol/var etc.. Now, prices ...


1

The VIX formula is based on Demeterfi et. al 1999 and their final variance swap replication formula is given by: $$ \begin{align}\label{eq:rep_formula} \mathbb{E}\big[\mathbb{V}\big] &= \frac{2}{T} \bigg[ rT -\left( \frac{S_0 e^{rT}}{S_\star} - 1 \right) - \ln \left( \frac{S_\star}{S_0} \right) \nonumber\\ &\quad+ e^{rT} \int_0^{S_\star} \...


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