medium · Quantitative Finance
Why is a geometric Asian option typically cheaper than an equivalent arithmetic Asian option on the same underlying?
- Geometric Asians admit a Black-Scholes-style closed form, so no such risk premium applies here.
- Averaging always dampens volatility versus the endpoint; geometric averaging dampens it more than arithmetic.
- Both averages have comparable sensitivity to the starting price; the AM-GM inequality drives the price gap instead.
- The geometric average of non-negative numbers is always less than or equal to the arithmetic average.
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