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Introduction - TURNBULL-WAKEMAN ASIAN The Turnbull–Wakeman formula is a well-known formula for continuous arithmetic average rate options. In many commodity and energy markets where Asian options frequently trade, the average is typically based on futures or forward prices, that is to say, the cost-of-carry for the underlying asset is zero. Options on stocks can also have a cost-of-carry of zero. If the continuous dividend yield is equal to the risk-free rate, then the extension given in this note can be used in that case as well. Turnbull-Wakeman was developed not only for Asian options with non-zero holding costs, but can also be extended to hold options on futures (with zero holding costs). In 2017, the European Energy Exchange announced that they had switched from using the Black-76 formula (Black 1976) for settling freight futures options to the Turnbull–Wakeman formula. From 2018 on, the European Energy Exchange has been settling both freight futures options and iron ore options based on our the modified Turnbull–Wakeman formula. |
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