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In the call case the payoff equals the amount by which the referenced variable x exceeds some fixed strike K
The payoff is zero if x falls below K
In the put case, everything is reversed so that x must fall below K for a payoff to occur.

The formal definition is as follows:
x is transformed into max{ ε(x-K) , 0 } where ε and K are constants defined in the contract specification.
Furthermore ε can take only the values 1 or -1 and corresponds to a product attribute called
K may take any value and is usually referred to as "strike".