Does one has to calibrate Black Scholes for FX Option Pricing?

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boulala

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Hey there,

my question is: If I want to calculate some FX Calls with Black Scholes or in more detail with Garman Kohlhagen, do I have to calibrate the Vol of the model to the market implied Vol? By calibration I mean something like the calibration of the five paramters in the Heston Model. In the Black Scholes there would be only one parameter, namely the Vol.

I mean when I take the strike, spot, maturity, interest rates and vol from the bloomberg terminal, I already have the implied Black Scholes vol from the market? Right? Is there any need for calibration?

In my opinion not, but maybe I am wrong.

regards
boulala
 
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? The answer is : it depends on what we need. For example, you need to get an option price from the volatility surface but for a (strike, tenor) point which is not quoted -> two approaches :
1. You select a model like the Heston one : your 5 parameters will be calibrated such that the semi-analytical formula gives back the market prices, and then these parameters + the formula will give you the price for the rest of the (strike, tenor) not quoted points
2. 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.

Rgds,
 
@Marcel Guina: Thanks for the very detailed answer. This helps me a lot! So if I understand you right, I just need to calibrate BS if I want to calculate options which strike/tenor is not directly quoted in the implied vola smile?

@Ken Abbott: Do you have a source, a paper or something else for me regarding the smile calibration issue with BS for FX?

Thank you both!
 
@boulala : Correct. Except that you do not calibrate BS, you calibrate the parameters of a model giving you the "smile" property, like the Heston model.
 
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