Barrier option
An option the payoff of which depends on the payoff to an ordinary option and whether a prespecified barrier has been crossed.
Asian option and look back options are also path dependent options.
Research Papers
Pricing Strongly Path-Dependent Options in Libor Market Models without Simulation
Chris Kenyon, DEPFA Bank plc, July 2008, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1253302
Connecting Discrete and Continuous Path-Dependent Options, 1999
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=140262
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