medium · Quantitative Finance derivatives

Why is a geometric Asian option typically cheaper than an equivalent arithmetic Asian option on the same underlying?

1. Geometric Asians admit a Black-Scholes-style closed form, so no such risk premium applies here.
2. Averaging always dampens volatility versus the endpoint; geometric averaging dampens it more than arithmetic.
3. Both averages have comparable sensitivity to the starting price; the AM-GM inequality drives the price gap instead.
4. The geometric average of non-negative numbers is always less than or equal to the arithmetic average.

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