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4

It depends what you exactly call Dupire's formula. If you take the original formula, valid under zero interest rates and dividends (or equivalently, considering undiscounted option prices on the forwards), which reads $$\sigma_L^2 = 2 \frac{ \frac{\partial C}{\partial T} }{K^2 \frac{\partial^2 C}{\partial K^2}}\,.$$ Then the formula for a put is the same, ...

1

I agree that the above mentioned eSSVI extension is a very efficient and elegant method for calibration purposes. Arbitrage free slices and interpolations can easily be created by making use of the criteria in the papers. It is also described in great detail in the thesis "Extending the SSVI model with arbitrage-free conditions" (google it). It ...

1

For the first question, there have been a number of improvements on SVI/SSVI that are much more flexible than SSVI and also come with easy-to-impose no-arb conditions. See below: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2971502 https://arxiv.org/pdf/1804.04924.pdf Paper 2 builds on Paper 1 and comes with a robust fitting procedure. One thing to ...

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