Geometric Asian Call (Kemna-Vorst)
Computes the price of a geometric-average Asian call option with the Kemna-Vorst closed form. Asian options pay based on the average price over the period, which reduces the impact of expiry manipulation and makes the premium cheaper. The geometric-average version has an exact solution: it's a Black-Scholes with volatility adjusted to σ/√3 and an adapted cost of carry. Enter the spot price, the strike, the interest rate, the term and the volatility.
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Geometric Asian Call (Kemna-Vorst)
Computes the price of a geometric-average Asian call option with the Kemna-Vorst closed form. Asian options pay based on the average price over the period, which reduces the impact of expiry manipulation and makes the premium cheaper. The geometric-average version has an exact solution: it's a Black-Scholes with volatility adjusted to σ/√3 and an adapted cost of carry. Enter the spot price, the strike, the interest rate, the term and the volatility.
When the average matters more than the end
A plain option looks only at the price on expiry day, which opens room for manipulation and for the bad luck of a single rough day. The Asian option fixes this by paying based on the average price over the whole period. It's widely used in commodities and FX, where what matters is the average price the company actually paid or received, not an isolated instant.
The arithmetic-average version has no closed form and requires simulation. But the geometric-average one does, and it was Kemna and Vorst who derived it in 1990. The trick is that the geometric average of a lognormal motion is still lognormal, which reduces the problem to a Black-Scholes with the volatility shrunk to σ divided by the square root of three and an adjusted carry.
Enter the spot price, the strike, the interest rate, the term and the volatility. The tool returns the geometric Asian call premium. It's usually lower than that of an equivalent plain option, precisely because the average smooths out the volatility, and it also serves as an approximation and lower bound for the arithmetic Asian.
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Computes the price of an arithmetic-average Asian call with the Turnbull-Wakeman approximation. Unlike the geometric average, the arithmetic average has no exact closed form, so Turnbull and Wakeman match the first two moments of the average's distribution and apply a Black-Scholes with adjusted volatility and carry. It's the market-standard approximation for arithmetic Asians, common in commodities and FX. Enter the spot price, the strike, the rate, the cost of carry, the volatility and the term.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.