Is this the correct value for the price of the call option?
In my opinion not, but maybe I am wrong. Hi Boulala, The volatilities that you get from your favorite provider are just implied vols, helping you to get using the BS formula an option price. You get basically a volatility surface of implied vols. But why one needs to calibrate on that surface? Why one needs a model if we have already these data sets? You select a model like the Heston one: You select the Dupire local vol model, which does not require any additional parameter, hence no calibration and gives you a bivariate function of volatility for any strike, tenor couple.
Then both gives you a process for the underlying FX rate. Only issue here is that Heston can also have moment explosions but that's another topic. I hope this helps. Do not hesitate if you have more questions. The smile calibration issue with BS for FX is well-known and probably well documented.
Thanks for the very detailed answer. This helps me a lot! It is GPL compatible. The software provides various facilities for computing values of financial instruments and related calculations. It is a major example of Mathematical finance. Its main use is in quantitative analysis. The financial instruments and derivatives it can evaluate include.
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