Numerical Methods for Implied Volatility in American Options

Summary

The document asks how to compute implied volatility for American options efficiently and accurately, especially when constructing volatility surfaces. It contrasts this task with European options, for which Peter Jäckel’s “By Implication” and “Let’s Be Rational” approaches are cited as fast, precise inversion methods. The post does not establish whether an analogous direct method exists for American options.

It frames the American option problem as two linked numerical choices: how to price the option, using a method such as a tree or Monte Carlo, and how to solve for the volatility that matches the observed price. The author favors a Brent root finder for the inversion step, then focuses the open question on finding a fast pricing method. No benchmarks, proposed solution, or accuracy comparisons are provided, so the text identifies the computational trade-off rather than resolving it. The pricing approach and solver may need to be assessed together for a specific surface-building workload.

Key ideas

• American option implied volatility requires repeated option pricing while searching for the volatility consistent with the observed price.
• The document separates the choice of pricing method from the choice of root-finding solver.
• Brent’s method is proposed as a candidate solver, while tree and Monte Carlo methods are mentioned for pricing.
• The post provides no benchmark or final recommendation for the fastest accurate combination.

Tags

# Fast implied volatility for american options


# Fast implied volatility for american options












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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.