September 26th, 2012, 6:00 am
QuoteOriginally posted by: chocolatemoneyQuote@chocolatemonkey ... the BCs are just Dirichlet. Hi, I have been playing with BCs.I would like to understand the meaning and the purpose of Zvan 1998 BCs (Finite Difference methods in FE dy Duffy on page 243), in particular the far-field BC for vol:According to my numerical experiments, it is much less robust that a simpler external BC, for example Heston 1993.It basically forces the user to make use of mollifiers or other tools (smoothing conditions, ..) to reduce the oscillations around the strike.Thanks!Most(?) articles do not motivate how they got these boundaries. In fact, formulating these PDEs on 1/2 infinite regions is mathematically incorrect IMO. Even more. no BC should be given as we should really be talking about NUMERICAL BC, of which there are many. You prescribe BC a posteriori, not a priori imo. Which BC has Roelof Sheppard in his thesis?Example: take FTCS scheme for u_t + au_x = 0 on 0 < x < infinity (a > 0) by approximation on (0,1). What numerical BC on x = 1?I do not understand the Zvan BC. Did you try domain transformation z = v/(v+1) and then examine Fichera BC at z = 1? As far as I can remember it becomes a characteristic boundary.In your post you seem to pose two issues:1. BC 2. Smoothing of payoff at the strikeAre these related here?//Who understands BC?
Last edited by
Cuchulainn on September 25th, 2012, 10:00 pm, edited 1 time in total.