Analytic Valuation Approaches for American Options

Summary

The document asks whether research on analytic pricing of American options continued after early papers on valuation properties. The response points to work presenting an exact explicit valuation for American put options. It characterizes the approach as an infinite sum of double integrals whose integrands are defined recursively.

This offers a lead for further study rather than a survey of the field. The exchange gives no derivation, numerical implementation details, comparisons with other methods, or evidence about how practical the representation is for pricing. Its scope is also specifically an American put result, so it does not establish a general closed-form formula for all American options. Readers would need to consult the cited paper and later research to assess the method and identify subsequent developments.

Key ideas

• The response identifies an explicit valuation approach for American put options.
• The cited representation uses an infinite sum of double integrals with recursively defined integrands.
• The exchange provides a research pointer rather than a complete review or derivation.
• The result described concerns puts and does not establish a general formula for every American option.

Tags

# Most recent work on American option **ANALYTIC** pricing


# Most recent work on American option **ANALYTIC** pricing












I am studying American options and inquisitive on why they lack an analytic pricing formula. I found a paper by Kim,1990 on analytic valuation of these options and then Byun,2005 paper which studies Kim,1990 analytic valuation properties.

I am afraid I have not found anything apart from that ever since 2005. Could this be the last document about the analytic pricing of American options.

(Perhaps I am mistaken or didn't do a thorough search). Could anyone suggest me some links to recent work on this area of Pricing American options using analytic formulae?

I appreciate in advance

## Answer by Mark Joshi (score 3)

https://quant.stackexchange.com/a/30169

An exact and explicit solution for the valuation of American put options SP Zhu 2006, Quantitative Finance 6 (3), 229-242

It's an infinite sum of double integrals with recursively defined integrands...

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