Forums > Pricing & Modelling > analytical approximation for double no-touch?

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 Strange Total Posts: 1639 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: 550 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: 1639 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: 104 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 One man's Theta is another man's Gamma - Me
 Strange Total Posts: 1639 Joined: Jun 2004
 Posted: 2020-01-21 00:08 @froloosBSM is good enough for what I am trying to do. Thank you 'Progress just means bad things happen faster.’
 ronin Total Posts: 550 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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