Turnbull–Wakeman Asian Option Approximation and Edgeworth Expansions

Summary

The document asks whether Turnbull and Wakeman’s approximation for continuously monitored arithmetic Asian options uses an Edgeworth expansion, and whether the method originated with them. The question describes the approach as matching the first two moments, then points to a textbook passage that appears to distinguish Edgeworth methods from Turnbull and Wakeman’s work.

The accepted reply says that Turnbull and Wakeman did use Edgeworth expansions and quotes a brief description of their paper’s goal: quickly pricing European average options by approximating the distribution of an average whose moments are easier to obtain than its full distribution. This supports the association between their method and Edgeworth approximation, but the exchange does not settle historical priority or explain the full formula. It also does not establish that matching only the first two moments is sufficient; the cited passage refers more generally to using available moments in an Edgeworth series. Readers seeking a derivation or precise account of the approximation’s assumptions would need the original paper or a more detailed source.

Key ideas

• Turnbull and Wakeman are associated in the reply with an Edgeworth series approximation for average options.
• The method addresses the difficulty of finding an average’s full probability distribution.
• The paper description emphasizes that moments of the average can be calculated readily.
• The exchange does not establish priority for the Edgeworth idea or provide the pricing formula.

Tags

# Turnbull & Wakeman Asian - not Edgeworth?


# Turnbull & Wakeman Asian - not Edgeworth?












My understanding is that Turnbull & Wakeman derived an approximation formula for continous arithmetic Asian option using Edgeworth series by matching the first two moments.

However, in the book Mathematical Models of Financial Derivatives, after a few pages of proof on the approximation, it writes "Besides the Edgeworth expansion method, .... Turnbull and Wakeman (1991) ..."

So the idea of Edgeworth approximation didn't come from Turnbull and Wakeman and possibly somebody else?

## Answer by jaehyukchoi49 (score 2, accepted)

https://quant.stackexchange.com/a/32575

Yes, AFAIK, they used Edgeworth expansions

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> The objective of this paper is to describe a quick way to price European average options. While it is very difficult to determine the probability distribution for the average, all of its moments can be readily determined. Thus, an Edgeworth series expansion can be used to approximate the distribution

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