ExchangeOneAssetForAnother Options
European 

where 

and where 
c = European call price S_{1} = Spot of asset one S_{2} = Spot of asset two b_{1} = Cost of carry asset one b_{2} = Cost of carry asset two Q_{1} = Quantity of asset one Q_{2} = Quantity of asset two T = Time till maturity = Volatility asset one = Volatility asset two = Correlation between the two assets N = The cumulative normal distribution function 
American 
Bjerksund and Stensland (1993) showed that an American Exchange one asset for another option (S2 for S1 can be priced using a formula for pricing a plain vanilla American option, with the underlying asset S1 with a riskadjusted drift equal to b1b2, the strike price equal to S2 , time to maturity T, risk free rate equal to rb2, and volatility equal to (defined in the same way as it is for the European option). 

See Also 
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