Apr
28

## Parisian option pricer

**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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