A path-dependent derivative is a contract with payoff that depends not just on the value of the underlying asset at maturity but on the entire history of the asset over the duration of the contract. Because of this dependency, the valuation of path-dependent derivatives is more complex than that of path-independent derivatives. In this chapter we consider the most common path-dependent derivatives: barrier options, lookback options, and Asian options, which were introduced in §4.11. The notation and assumptions of the preceding chapter are still in force.
Recall that the payoff for a barrier option depends on whether the value of the asset has crossed a predetermined level called a barrier. ...
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