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One does not estimate the local volatility at a given $T$ and $K$. Instead, Dupire's formula actually gives $\sigma(T,K)$ for all $T$ and $K$. $$ \sigma^2(t_0,S_0;T,K)= \frac{\frac{\partial C}{\partial T} + (r - q)K \frac{\partial C}{\partial K} + qC}{\frac{1}{2} K^2 \frac{\partial^2C}{\partial K^2}} $$ where $C(t_0,S_0;T,K)$ are the call prices for ...


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For short maturity SPX option chain, the analytic form of the V-shape volatility smile has been fully worked out in my latest paper on SSRN. You can take a look.


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I'll address your questions in order: 1a) For TSRV constructed using high frequency returns from NYSE market open to market close on a single day, the output should be numbers on the order of magnitude of 1e-4 to 1e-5. In other words, your numbers look about right. I got these number from calculating TSRV for IBM data myself using Kevin Sheppard's MatLab ...


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This is a result of Ledoit et al Lemma proof in Appendix of http://www.ledoit.net/9-98.pdf


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Local volatility trats volatility as a function of price (St) and time (t), considering volatility constant. It means that you are building a volatility surface depending on price and time. What you are doing is given a certain value of volatility, what will be the price in Xdays long, or viceversa. If you are dong market making with plain vanilla ...


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Instead of just considering a parallel shift of the whole volatility surface, you can decompose the surface into maturities/strikes domains, so called buckets and consider Vega buckets which are sensitivities wrt to bumps of each of these domains. The vol smile is often inter/extra-polated using a model calibrated to market prices, e.g. the SABR model or ...


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I know one article (download) that explaining how to calculate local vol surface from IV surface and also chapter 18 of this book is very good In this context. However you know that Dupire’s (1994) formula for local volatility is \begin{align} \sigma_L(k,T)=\sqrt\frac{\frac{\partial C}{\partial T}}{\frac{1}{2}K^2\frac{\partial^2 C}{\partial K^2}} \end{align} ...



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