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Delta Volatility Surface Usage to value the option

1 ) Since you look at commodities, these are options on futures. Hence modelled with Black76 - greeks are here at the end. If options are quoted in price, one can solve for IVOL. Likewise, if IVOL is ...
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Interpolating implied volatility term structure when IV is sampled at fixed delta points

The iso-moneyness approach guarantees no arbitrage in terms of calendar spreads, but it is not proven it does not introduce some butterfly spreads at some interpolated time. See Arbitrages in the ...
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Calibrate the SABR model to the implied volatility surface

This is absolutely something you can do. However, I've never once seen a market in which this is practically a useful thing to do. When parameters get calibrated smile-by-smile, vol of vol is often ...
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Calibrate the SABR model to the implied volatility surface

In this paper you might find some answers to your question: https://www.researchgate.net/publication/319205444_MANAGING_VOL_SURFACES

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