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Strange


Total Posts: 1648
Joined: Jun 2004
 
Posted: 2020-01-18 17:02
I recall there is an analytical approximation for double-no-touch option. Does anyone remember what it is or can point me to a reference?

'Progress just means bad things happen faster.’

ronin


Total Posts: 585
Joined: May 2006
 
Posted: 2020-01-18 23:13
Double no touch calls and puts?

The formula is a bit long. It's in Haug's book under the name Call/Put Up-and-Out-Down-and-Out.

But these analytical formulas are a waste of time. Its easier to just run a pde solver in excel. And much more accurate. And stable.


"There is a SIX am?" -- Arthur

Strange


Total Posts: 1648
Joined: Jun 2004
 
Posted: 2020-01-18 23:22
Yeah, double KO call/put is what I want - a digital DnT can be decomposed into a pair of these. I can probably put together a better model, but this is as much as I need at the moment.

'Progress just means bad things happen faster.’

frolloos


Total Posts: 121
Joined: Dec 2007
 
Posted: 2020-01-20 16:51
Under Black Scholes or SV?

Under BMS assumptions see formulas (13) - (15) in link below, which are the formulas ronin meant I think.

http://www.espenhaug.com/BarrierTransformations.pdf

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Strange


Total Posts: 1648
Joined: Jun 2004
 
Posted: 2020-01-21 00:08
@froloos

BSM is good enough for what I am trying to do. Thank you

'Progress just means bad things happen faster.’

ronin


Total Posts: 585
Joined: May 2006
 
Posted: 2020-01-21 20:21
I really wouldn't bother with it.

If you buy the book, you get Haug's own spreadsheet with these formulas already coded up. So you can't even blame yourself for messing up a simple formula. But the profiles still look nothing like they should.

There is lots of subtract-two-exponentially-large-numbers-to-get-an-exponentally-small-number-then-take-the-log-to-get-order-1-number etc.

"There is a SIX am?" -- Arthur
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