Hi Henry,
At the time being QL does not support discrete barrier monitoring and it will take a bit of work to get it running. Barriers are forward skew sensitive products and therefore the question which market model to use (Local Vol, stoch Vol or local stoch vol) is more important than the difference between daily or continuously monitored barriers. Also in the equity world the price of a barrier is very sensitive to your dividend modelling. As long as your spot is not very close to the barrier I'd spent most of my time on these points and afterwards incorporate the daily observation feature. IMO people still tend to use "barrier adjustments" to do this, e.g. see the "original" paper http://www.columbia.edu/~sk75/mfBGK.pdf
If you want to implement the correct monitoring then to start with I'd use free boundary conditions and a standard mesher, which is also used to price plain vanilla options. The daily monitoring of the barrier can be incorporated by a StepCondition for every day. Please have a look into fdmlinear.cpp, class FdmHestonExpressCondition and the test case testFdmHestonExpress. In this test case a "barrier" is monitored every 4 months and a corresponding cashflow is initiated if the corresponding triggerlevel (barrier) is exceeded. You'll need to implement the corresponding barrier step condition.
hope this helps
Klaus
On Tuesday, July 23, 2013 07:29:26 PM Peter Caspers wrote:
Hi Henry,
I am not sure if I fully understand what you have in mind, also Klaus is for sure much more the person who is qualified to answer.
What you can do with the class is to specify a boundary condition which may be a function of time t. This condition applies to the boundary
of the PDE (and to nowhere else). In addition the region in which you can solve PDEs in ql is restricted to the direct product of intervals, if I
am not mistaken.
Does that help a bit ?
kind regards
Peter
On 23 July 2013 07:42, Haoyun XU <[hidden email]> wrote:
Hi Peter,
I have a question regarding your FdmTimeDepDirichletBoundary class:
How can I apply the boundary constraint to a range of points near the boudary, instead of the exact point on the boundary?
More specifically, think about the pricing of discretely monitored (daily) barrier options. Suppose we are using finite difference engine on a grid from Smin to Smax. We have ordinary Dirichlet boundary for each intraday time slice. However, for day-end time slice, extra constraint should be applied. For example, up&out put options should have 0 value for underlying price between barrier
and Smax.
Any ideas how can I handle this using existing QuantLib framework?
Best,
Henry
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