Hi all,If you had to price two options on the same underlying, strike, expiry, etc. the only difference would be that one option would be american and the other european. Would you use the same implied volatility? Thanks! Matt

I'm a little confused what you're asking. When you price option using implied vol, you always get the "right" price (ie. the market price). Since implied vol is the vol you put in BS so that market price and BS price matches. Therefore, if you want to find out option value is and uses implied vol, you might as well just look at what market price is. nonetheless, I would also expect implied vol for american and european are different. If you're trying to delta-hedge an option and interested what happens when you put wrong volatility into BS, I suggest you to read PWQF2 volume 1 chapter 18 for a detailed discussion. The main result is that on average, it doesn't matter the Vol input is wrong. The expected P/L is roughly constant; the actual P/L however, is random, and the variance depends on the input Vol.

No. The vol is the parameter controlling the distribution of the spot at the boundary of your integration domain. It is quite simple for a european option, however it has a funnier shape for american options, hence you will be sensitive to term structure (american options have shorter duration) and skew (since at some points early exercise decision will be base on spot).If you know the full surface of european prices/vol, you can calibrate your favorite vol model and integrate the payoff (eg with local vol) of the american.Now the funny thing is that you usually can only observe american prices (at least for short date maturities and stock options). Now you are left with the inverse problem, which is a little bit trickier than bilndly applying Dupire formula.

Not to disagree with islington at all, I think that momentumpartners might want a simpler answer, too:If you are in a true Black-Scholes world (so flat skew, flat term-structure, constant vol), then to calculate the American option price, you want to use the same volatility in your tree/finite-difference engine/AMC/Ju-Zhong approximation/method-of-your-choice as the implied vol of the European option.

thanks guys! helps a lot. So is there a way to compare an european option's implied vol with an american option's?tks

Yes, sometimes. To summarize:Pure BS world: the vols are the same for American and European.Anything else: highly model dependent; all bets are off.

so in the real world how would you do? for example let's take an ADR like NOK that has (American) options listed on the US market and NOK1V FH that is the local stock trading in Finland and has options listed too but European. Let's assume that the EURDOL rate is constant and is equal to 1. So imagine here you get implied vols that are not the same in Europe and in the US. How would you compare them?

You would need a model for the stock-price process (ignoring all the basis risk issues and ADR/underlying arbitrage limitations which may matter more than the American/European model differences, by the way - this is not my field of expertise). You would calibrate this to one set or the other (European or American) and you would see how the prices of the set you didn't calibrate to look.

thanks! that's a good idea. but a lot of work at the same time! what is your expertise?

My expertise is energy/commodities, credit and rates.It is a lot of work but, if it were too easy, there wouldn't be many good jobs for quants! And I have expensive tastes...

haha tks mate