The basket value is written , using the price and weight of asset . The payoff of a call at expiry is the amount by which the basket value exceeds the strike price.
Consider a hypothetical example in which a call (strike price 100 yen) is written on a basket of stocks X and Y at weights of 0.5 each. If X is 130 yen and Y is 70 yen at expiry, the basket value is 100 yen and the payoff is 0 yen. If X is 130 yen and Y is 120 yen, the basket value is 125 yen and the payoff is 25 yen.
The lower the correlation between the assets, the smaller the variation in the basket value. When the weights are positive and the strike price of the basket equals the weighted sum of the strike prices of the individual assets, the premium of a call is at most that of the combination of calls on each asset. The price is evaluated by approximating the distribution of the basket or by the Monte Carlo method.