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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 ...

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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 ...

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No, this is a very rough approximation, ignores convexity. Consider this: if some CDS spread changes from 30 bps to 31 bps, it's a much bigger deal than if it changes from 300 bps to 301 bps. You should bite the bullet and get the ISDA CDS standard model to run. (You can actually download an Excel add-in if you don't want to compile C++ code, but you really ...

4

OK, here is a simplified demonstration: Before we consider swaps, let us consider very simple bonds. Suppose that you have a choice of two zero-coupon bonds. A riskless one costs 95 and is certain to pay 100 in 1 year. A risky one costs 90, is expected to also pay 100 in 1 year, but with some probability $p$ will default and only pay some $R<100$ on the ...

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