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There are multiple ways of calibrating a term structure model. The main approaches are:- minimize sum of squared price errors- minimize sum of squared implied black volatility errorsAny ideas what method is better for what and why?

That is a good question. I have seen both approaches, but most traders seem to go for calibration on the vol surface, as they tend to 'understand' the implied vol surfaceI have also seen an analysis showing for a specific model in a specific product in a specific backtest (I admit, this is not really general), that the calibration to implied vol outperformed in the hedging strategy

do you have a link to that analysis?thanks!

My two cents : when you're very out of the money, the price of the option does not really depend anymore on the volatility of the underlying. So minimizing on the vol might give some weird results if the set of option is too large.

my 2c are close to antonio'sfar-OTM or far-ITM options are converging to their intrinsic value, regardless of the modelany model really models the time value of the contractsmall price differences ITM or OTM (which could be due to illiquidity, microstructure etc) will cause large IV differences. relying on that area will not convey anything really meaningfulKyriakos

You can add weight in the chi square, looking for something which is symetric between OTM and ITMto match time values. The most relevant point to use in calibration are those really sensitive to volatility,(eg the one with great vega) so component proportional toor equivalentlylook better for calibration.Mars

QuoteOriginally posted by: MarsYou can add weight in the chi square, looking for something which is symetric between OTM and ITMto match time values. The most relevant point to use in calibration are those really sensitive to volatility,(eg the one with great vega) so component proportional toor equivalentlylook better for calibration.MarsThat's very interesting... I generally calibrate to minimise the percentage mean squared error instead of the absolute Sum((PriceModel-PriceMarket)/PriceMarket)^2(the rationale is that prices can change by more than a factor 10 between short and long maturities). Should I still divide the percentage error by vega to take care of the sensitivity to volatility? Or is it that if I move from absolute to percentage errors this is not correct anymore?thanks

I always thougt about it like this: even if vol is the quoting devise, your traders will ultimately trade in cash, and any calibration error will show up in the P&L in cash (if you do it properly). So this is where you want to be close to, IMHO.

I personally would go for volatility calibration according past experience.

QuoteOriginally posted by: probablyI always thougt about it like this: even if vol is the quoting devise, your traders will ultimately trade in cash, and any calibration error will show up in the P&L in cash (if you do it properly). So this is where you want to be close to, IMHO.I used vega^2 to weight. Anyone tried both weighting of vega and vega^2?Thanks,Best Regards