Spread Option (Kirk Approximation)
Computes the price of a spread option with Kirk's approximation: a call on the difference between two assets, S1 minus S2, with a strike. Spreads are everywhere in commodities (oil crack spread, power spark spread) and no exact formula exists, so Kirk proposed a clever approximation that reduces the problem to a Black-Scholes with an effective volatility combining the two vols and the correlation. Enter the two forward prices, the strike, the volatilities, the correlation, the rate and the term.
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Spread Option (Kirk Approximation)
Computes the price of a spread option with Kirk's approximation: a call on the difference between two assets, S1 minus S2, with a strike. Spreads are everywhere in commodities (oil crack spread, power spark spread) and no exact formula exists, so Kirk proposed a clever approximation that reduces the problem to a Black-Scholes with an effective volatility combining the two vols and the correlation. Enter the two forward prices, the strike, the volatilities, the correlation, the rate and the term.
Betting on the difference between two prices
Much of the commodity world revolves around spreads, not absolute prices. A refinery profits from the difference between crude and gasoline (the crack spread); a power plant, between fuel and electricity (the spark spread). A spread option pays on that difference, and pricing it is harder than a plain option, because it involves two correlated assets.
The problem is that no exact closed form exists for the spread option. In 1995, Kirk proposed an approximation so good and so simple that it became the market standard: it rewrites the problem as a Black-Scholes on a ratio of the assets, with an effective volatility that combines the two individual volatilities and the correlation between them. The more correlated the assets, the more stable the spread and the cheaper the option.
Enter the forward prices of the two assets, the spread strike, the two volatilities, the correlation, the interest rate and the term. The tool returns the premium by Kirk's approximation. Being an approximation, it loses a little accuracy for strikes far from zero, but it's excellent for most practical cases.
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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.