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by Seagulls
August 4th, 2019, 2:46 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

With the exception of horizontal lines and maybe parabolas, I believe everything else requires numerics. 
OK. Thank you, Alan.
by Seagulls
August 3rd, 2019, 8:26 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

Alan, the simple solution (for me) would be the ability to determine the probability that a BM will hit a non-horizontal straight line. I would then be able to work my way round the arc and, in effect, be able to aggregate all the probabilities.
by Seagulls
August 3rd, 2019, 3:32 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

I think GBM can hit every point on that circle! -- well, possibly excepting one, which doesn't matter. DavidJN's cite may be spot-on, although I haven't looked at that paper in years.  Off-hand, the horizontal line through A identifies two key times (t1,t2), and the GBM's location at t1 splits the ...
by Seagulls
August 3rd, 2019, 3:29 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

Now I'm with Alan.
Thanks for your time, bearish. 
by Seagulls
August 2nd, 2019, 6:02 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

https://www.dropbox.com/s/96sbappmcaial4o/GBM%20hitting%20Arc%20CHD.png?dl=0 The problem is establishing the probability of the asset price (moving in a GBM) hits the circle, which in effect means it hits the arc CHD. The circle is static with centre A and radius AC and the current asset price is kn...
by Seagulls
August 2nd, 2019, 5:06 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

I was imagining something like two (possibly log) exchange rates (FX - given the "one-touch" terminology) X and Y, with the barrier being defined in terms of [$] X^2+Y^2=c [$].  This feels like it would lead you into Bessel processes and the like, but probably well covered in the probability theory...
by Seagulls
August 2nd, 2019, 5:04 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

To me, a circle requires two dimensions. What are the two dimensions? 
Alan, I've been through the index and it looks like a must-have book. Unfortunately I don't think it addresses my problem which I've covered with a diagram below. Thanks anyway.
by Seagulls
August 2nd, 2019, 4:53 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Re: Circular barrier

Try Kunitomo and Ikeda (1992), which is likely referenced in more recent papers.
Thank you for the reference. I'll check it out.
by Seagulls
August 1st, 2019, 6:22 am
Forum: General Forum
Topic: Circular barrier
Replies: 14
Views: 3827

Circular barrier

Does anyone know of an article which prices a GBM one-touch option hitting a barrier that is circular in shape? Thanks.
by Seagulls
March 1st, 2018, 10:43 am
Forum: General Forum
Topic: Path dependent historic volatility
Replies: 1
Views: 548

Path dependent historic volatility

I'm no mathematician and feel a bit of a fraud being on here. I am developing a retail trading platform for limited risk CFD which involves a combination of short term path independent and path dependent options. To price the path dependent options I have used an iterative process involving a DNT wi...
by Seagulls
March 7th, 2011, 6:10 pm
Forum: Technical Forum
Topic: Volatility for fx binary options
Replies: 6
Views: 22806

Volatility for fx binary options

Just about, assuming you're ONLY trying to value an ATM option.
by Seagulls
March 7th, 2011, 1:18 pm
Forum: Technical Forum
Topic: knock-in knock-out option
Replies: 7
Views: 193069

knock-in knock-out option

((Down-and-out one-touch call - Up and out one-touch put) + 1) / 2.
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