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Turnbull–Wakeman Approximation for Asian Options on Futures

Article Quant Q&A · Author: ionpoint
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Summary

The document identifies a method for pricing continuous arithmetic-average options when the underlying is a futures contract. It describes adapting the Turnbull–Wakeman approximation, which is commonly used for arithmetic Asian options, to the futures-option setting under a Black-style pricing model.

The response points to a related derivation but does not reproduce its proof, so the document offers a direction for further study rather than a step-by-step justification. It cautions that the approximation has limited accuracy outside lower-volatility settings and shorter maturities, noting that performance is reported as good around 20–30% volatility and for tenors up to two to three years. Those stated ranges are guidance, not a general guarantee; the note supplies no validation data, assumptions, or comparison against other pricing methods.

Key ideas

  • The Turnbull–Wakeman approximation can be adapted to price continuous arithmetic Asian options on futures.
  • The approach is relevant to implied volatility adjustments within a Black-style futures option model.
  • The response refers readers to a related derivation rather than presenting a proof.
  • The stated accuracy is limited, with the approximation described as working well mainly at lower volatility and shorter tenors.

Tags

OptionsFuturesDerivatives pricingVolatility
Full text
# Implied volatility of Asian options under Black76 model


# Implied volatility of Asian options under Black76 model












I found this repository (options pricing in Python) where they adjust IV for Asian options and they use it under the regular BS76 model.

I could not find any proof of this result on the web, do you know any paper where a similar result is proved or do you have any idea from where to start?

Thank you

## Answer by Hasek (score 4, accepted)

https://quant.stackexchange.com/a/71203

This is the Turnbull-Wakeman approximation for pricing continuous arithmetic average options adjusted for the case of option on futures. Please note that this approximation has some serious limitations and works well for low volatilities ($~20-30\%$) and short tenors (up to $2-3$ years).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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