Ali Hirsa

Morgan Stanley, New York

**Why Be Backward: Forward Evoluton Equation for Barrier Options**

In a pathbreaking work, Dupire (94) developed a forward equation (as opposed to a backward
equation) for European option values. We extend Dupire's analysis to barrier options with jumps
in the underlying asset. This extension allows us to efficiently value a portfolio of barrier
options or to determine evoplution parameters from market prices of barrier options.

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