Dear All, I modelled a vanilla european FX Option on Bloomberg (100mm USD Call/CNH Put 2Y 6.5) using Black Scholes, Volga Vanna, Stochastic-Local Vol models available on Bloomberg OV screen.I get very different results.BS: 1.73mm USDVV: 1.82mm USDLSV: 1.90mm USDI am unsure how to interpret this difference given they are vanilla european options. My understanding is - the starting point of modelling is the (actionable) option prices which derives BS vol surface. This vol surface is then used to calibrate VV/LSV.However, if the pricing result from the model is not the same as starting point option prices then there is a disconnect.Here are my questions:- Should I expect prices to be the same using BS, VV, LSV for vanilla european options? and accordingly Bloomberg implementation is incorrect- Is it the case that prices for vanilla european options will be different using BS, VV, LSV given they are different modellign frameworks. In which case, how do I interpret the difference to starting actionable option prices? Would appreciate your thoughts. Rgds,

Hi,as I know, the VV is calibrated only on the 3 market quotes ATM, RR25, BF252vol, so you don't have the calibration to the full volatility smile/surface. On the other side, the LSV should be calibrated on the whole surface and a difference with the BS price can be seen as a calibration error IMHO.

So in other words, are we saying in an ideal world, prices for vanilla european fx options using BS, VV, LSV, or any other better model should be the same?

Comparing prices is meaningless. Calculate vega of each price with one of the models, and then divide difference in price by the vega. That should give you information what would be a difference in implied vol from the resulting prices, so you will have information how much those models differ in interpolation of the surface. Basically you have liquid only ATMF, and 25 delta call and put derived from risk reversal and BFLY. Some currency pairs would have probably some liquidity on 10 delta. All other points are simply interpolated or extrapolated by various means, I guess your BS is using some splines, VV is solving a system of equations or using a second order approximation in implied vol to solve it, and LSV is using some FDM engine to solve the model, but when it is used for vanilla option, it is just a bit more sophisticated method of interpolation, as long as you are interested only in price. The reason to use any of the methods is related to your belief, which of tchem gives you more appropriate hedge ratios.Answering your question, there are maximum three points, where vanilla prices from BS and VV should be exatly the same, and LSV should not differ by more than a few bps of vol. All other points may differ, typically in the region of 25 delta put to 25 delta call only by a few bps of vol, but on the wings they will diverge. in LSV there is a high Chance, that the implied smile will by comming out from SV, to wings will be increasing, while from VV the wings are flattening in extrapolation.

Thanks pimpel, this is very useful. Just to close this one, I priced a vanilla USDCNH using strike corresponding to 25DFwd (in BS framework) - controlled experiment.Results as follows: Mkt Val Vega Diff Num Vega (BS)BS 1,204,141 457,556 VV 1,250,766 329,082 46,624 0.10 LSV 1,422,893 296,997 218,752 0.48 I am assuming remaining noise is because of model implementation?Related question - delta (and other greeks) is very different based on the choice of model.BS 25%VV 11%LSV 50%for a sell side desk trying to hedge a large FXO portfolio, what is typically done to compute exposures? Use same modelling framework (LSV?) for consistency across all options?

results didn't look aligned. posting them separately Mkt ValBS 1,204,141VV 1,250,766LSV 1,422,893 VegaBS 457,556VV 329,082LSV 296,997 $Diff to BSBS VV 46,624LSV 218,752 Num Vega (BS)BS VV 0.10 LSV 0.48

Regarding hedging your fx option book, you should always have a consistent model for all positions. It is pointless to calculate delta from BS for European vanillas, and from LSV for barriers, because you will compare pears with apples, as both models have different assumptions. You could refer to:Mercurio, Fabio and Morini, Massimo, A Note on Hedging with Local and Stochastic Volatility Models (November 3, 2008). Available at SSRN: http://ssrn.com/abstract=1294284 or http://dx.doi.org/10.2139/ssrn.1294284 or http://www.fabiomercurio.it/fxbook.pdfWhat is the unit of your Vega? Is it related to change in price for a unit change in vol, for a 1 p.p. or one bps of vol?

Thanks. Unit for Vega is USD per 1% vol move. So vol moving from say 4.5% to 5.5%.

As you see from results, your vegas are model dependent. Since you want to compare different models with BS price, let's take the BS vega. If you divide your price difference by your BS vega, you get information that in order to have a BS price equal to your VV price you would have to change your implied vol by 0.1 p.p. (with first order accuracy). Your LSV differs from BS price by 0.48 p.p. (or 48 bps). With such information you can assess accuracy of your pricing model when you compare with tipical Bid/Offer spreads on a given expiry and delta levels. Pricing should not worry you much. I would rather design a back-test on your P&L to identify which model gives you deltas with most accurate (and cheapest in implementation) hedge ratios.

Thats fair comment from a sell side perspective. However, Valuation is more important than delta/hedging from a Buy side perspective, hence need to worry about it.. (I'm from buy side)