Geometric Asian Options: Market Use and Their Role in Pricing
Summary
The document distinguishes geometric Asian options, often introduced in textbooks because they admit an explicit Black–Scholes pricing formula, from the contracts used in practice. The answers disagree somewhat about whether geometric Asian options trade over the counter: one describes exotic options as dealer contracts, while another says geometric averaging is not traded, even OTC. The distinction should therefore be treated as a point of disagreement in the discussion.
The clearer practical contrast is with arithmetic Asian options, which average an underlying’s price over time and can be useful when buyers care about average purchase costs, such as for fuel or repeated currency purchases. Averaging also reduces effective volatility and can make an option cheaper. Geometric Asian pricing remains useful as a tractable approximation or as a control variate in Monte Carlo estimation of arithmetic Asian prices. The examples are qualitative; the document gives no market survey or detailed pricing evidence.
Key ideas
- A geometric average can make Asian option pricing analytically tractable under Black–Scholes assumptions.
- The answers differ on whether geometric Asian options are traded OTC.
- Arithmetic Asian options may suit commodities or currencies bought continuously over a period.
- Geometric Asian prices can support approximation or variance reduction when estimating arithmetic Asian values.
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Full text
# Which stock tick has its geometric asian call? # Which stock tick has its geometric asian call? Many finance books introduce the pricing on geometric asian call/put options underlying black-scholes model, since its price has its explicit formula. I am not sure, if geometric asian option is indeed traded in the real market, or otherwise, it is merely an academic interests. If it is traded, which stock (ex. AAPL) has its geometric asian option? ## Answer by Alex C (score 3, accepted) https://quant.stackexchange.com/a/43512 Asian options are based on the average price of something during a period. The average price of a stock is not very interesting, so Asian options on stock are not traded. The average price of oil (or other commodity) during a season is important because it determines the cost of heating or transport when you burn fuel constantly during the season. Similarly the average price of a foreign currency is important if you are constantly making small purchases of foreign currency during the year. For this reason it may be interesting to have Asian options that can be used in these situations. So Asian options tend to be on this kind of continuously purchased commodity, not on stocks like AAPL. ## Answer by AlRacoon (score 3) https://quant.stackexchange.com/a/43508 This is an example of an exotic option. These are not listed and traded on any exchange. Rather they are traded in what is called the over the counter market. The dealers will trade these by entering into a contract with clients. ## Answer by jherek (score 3) https://quant.stackexchange.com/a/43518 They are not traded, even Over-The-Counter (OTC). Asian options with arithmetic averaging are traded. The geometric Asian may be used to derive a closed-form approximation for the arithmetic variety, or as a control variate in a Monte-Carlo simulation to significantly reduce the variance of the estimate. Arithmetic Asian options are interesting, not only for commodities, but also for stocks, as it decreases the effective volatility, and thus makes the derivative cheaper and less risky. In Asia, because the markets are more volatile, it is common for example to settle on a 5 days averaging period before the maturity date.
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