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There is no difference in information, though the fitting algorithm may increase in complexity. First note that in practice you never have an entire curve or surface of prices $C(K,T)$ of any kind of option. You only have a finite number of observations and even those typically have a bid and an offer. I would therefore argue that the correct picture of ...


The Price of an American option may contain information on the expected behaviour of it's holder. When might he/she exercise the option ? Contrary to European options that don't. Thus when you are primarily interested in "reconstructing" the transition density - I would stick with the European-Option-Prices. If however you were to price path dependant ...

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