Peter Jäckel has developped a method to compute implied volatilites from option prices, called "by implication", see the papers :
- By Implication
- Let's be Rational
on its website -- as well as a normal vol implying study/method (see the paper "Implied Normal Volatility").
They all concern european options, and the "by implication/let's be rational" method, even if it is simply based on the profile of the function to invert, is regarded as the quickest/most precise among practioners, especially among people constructing implied vol surfaces.
My question is : is there an analogue for the implied volatility of american options ? What's the best method (precision+speed) to do this ? (The context is the construction of implied vol surfaces.)
There is a choice of numerical method to compute the price (MC, trees, whatever) + type of solver of back out the implied vol. As the faster the solver the better I'd go for a Brent for it, which would leave only the choice of the quickest way to price the american numerically.