Why Asian Options Use Average Prices

Summary

The document explains the intuition behind an arithmetic-average Asian call payoff. In practical contracts, the average is typically formed from daily stock prices observed during a specified period near the option’s end, rather than from a continuously sampled path as in the integral expression in the question.

Averaging can make the payoff less sensitive to a single closing price. The document links this feature to reduced scope for a dealer to influence whether the option finishes in or out of the money by moving the underlying at expiry, especially in a small market. It also notes that the average price is less volatile than the individual stock price, which can lower the option’s cost and appeal to investors expecting price gains. These are motivations, not a full valuation treatment: the text gives no pricing formula beyond the payoff definition, and the actual averaging schedule depends on contract terms.

Key ideas

• An arithmetic-average Asian call pays on the average underlying price relative to the strike.
• Real contracts commonly calculate the average from daily prices over a specified period near expiry.
• Averaging reduces dependence on the price at a single expiration moment.
• Lower volatility of the average can make an Asian option cheaper than a comparable conventional option.
• The averaging schedule and contract details are not specified by the general payoff expression.

Tags

# Asian option and option pricing


# Asian option and option pricing












I know Asian option is defined as follow $$\left(\frac{1}{T}\int_{0}^{T}S_t dt-K\right)^+$$ Is there a good idea behind this definition.

Thanks.

## Answer by Dom (score 2, accepted)

https://quant.stackexchange.com/a/29480

This is the standard textbook definition for the payoff of an arithmetic average Asian call option.

In reality the average will be based on a daily average of stock prices over some period at the end of the life of the option.

The first "idea" behind Asian options is that the payoff is harder to manipulate by dealers - the story is that in certain small markets dealers were able to push down the stock price at expiry by selling shares and so move options out of the money. If the final payoff is based on an average then this is harder to achieve.

The second "idea" is that the volatility of the average of the stock price is lower than the volatility of the stock price. This makes the option cheaper and so more attractive to investors who believe that the stock price will rise.

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.