Fairmat Example

Path-dependent Swap

A "path-dependent" option is an option whose value depends on the sequence of prices of the underlying asset rather than just the final price of the asset. An example could be a "ratchet" cap, a type of nonstandard cap which incorporate rules for determining how the cap rate for each caplet is set, following this type:

K_t+1 = K_t + spread.

In this tutorial we show a swap in which the payment of one of the parties takes the formula set out above, but the spread is a function of the 3-Months Euribor . In formula:

Option(t+1) = Option(t) + spread(t+1),

where spread(t+1) depends on the value of the 3-Months Euribor  at time t+1.