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Apr 28

Parisian option pricer

Posted by abiao at 15:14 | Code » Other | Comments(0) | Reads(8262)
Parisian option might sound unfamiliar to you, it is basically a barrier option but becomes activated only after stock prices have spent a certain continuous, pre-decided time, called a window, above or below the barrier. One of possible motivations for the existence of the Parisian option, as stated in Haber, Schoenbucher, and Wilmott (1999) is: "...there is a need to make the option more robust against short-term movements of the share price..., in particular, it is far harder to effect the triggering of the barrier by manipulation of the underlying..."

Taking an up barrier Parisian option as an example, the barrier time tau is defined as the length of time the stock prices have been above the barrier in the current excursion
tau := t − sup {s <= t|S(s)<= L}
with up barrier L, tau measures the difference between the current time t and the last time the stock price S below L, the call feature is activated only if tau>= D, with D being barrier window.

Interested reader shall download a Parisian option pricer at http://paul.wilmott.com/software.cfm, where the authors price Parisian options by a finite-difference solution of a three-dimensional partial differential equation.


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