# Computing stop probability Classic List Threaded 5 messages Reply | Threaded
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## Computing stop probability

 Maybe a naive question but given the price and SD of an asset, is there a way to calculate the probability of hitting a stop set at X over the next N days? I know making appropriate assumptions, this is a Wiener process but can't find the correct equation. A) Is there a closed form solution for this? B) Is there an R function related to this? Ernie Sent from my iPhone _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Computing stop probability

 You might want to check out the derivation of the Thorp / Black-Scholes-Merton formula as it deals with essentially the same concepts... On Wed, Nov 25, 2015 at 11:27 AM, Ernest Stokely <[hidden email]> wrote: > Maybe a naive question but given the price and SD of an asset, is there a > way to calculate the probability of hitting a stop set at X over the next N > days? I know making appropriate assumptions, this is a Wiener process but > can't find the correct equation. > > A) Is there a closed form solution for this? > B) Is there an R function related to this? > > Ernie > > Sent from my iPhone > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R questions > should go. >         [[alternative HTML version deleted]] _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Computing stop probability

 On Tue, Nov 24, 2015 at 6:31 PM, Nick White <[hidden email]> wrote: > You might want to check out the derivation of the Thorp / > Black-Scholes-Merton formula as it deals with essentially the same > concepts... > > On Wed, Nov 25, 2015 at 11:27 AM, Ernest Stokely <[hidden email]> > wrote: > >> Maybe a naive question but given the price and SD of an asset, is there a >> way to calculate the probability of hitting a stop set at X over the next N >> days? I know making appropriate assumptions, this is a Wiener process but >> can't find the correct equation. >> >> A) Is there a closed form solution for this? >> B) Is there an R function related to this? >> Black-Scholes (and stochastic volatility extensions) can give you a probability of hitting a price under the equivalent martingale measure ("Q") but that can be pretty far from the "real-world" ("P") probability of the same event happening. Or it may be close, depends on your market. If you don't want to do the math (it really is easy though -- half a page at most), the relevant delta is decent approximation. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Computing stop probability

 In reply to this post by wizardchef1 Ernest Stokely <[hidden email]> [2015-11-24 16:28]: > Maybe a naive question but given the price and SD of an asset, is there a way to calculate the probability of hitting a stop set at X over the next N days? I know making appropriate assumptions, this is a Wiener process but can't find the correct equation. > > A) Is there a closed form solution for this? > B) Is there an R function related to this? A) NAFAIK. My solution using iteration is here: http://www.nosyntax.net/cfwiki/index.php/Probability_of_Touch-lognormal-3Note that this is not the same as the probability the price is not less than X N days hence. HTH, -rex -- Classical economists look for their keys under a streetlight after losing them in an alley. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
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## Re: Computing stop probability

 In reply to this post by Michael Weylandt I misread your question: delta is only an approximation to being below a level at a fixed time, not during an interval. If you want the probability of hitting a stop over an interval, you want the running max (or running min -- Weiner process is symmetrical) of a Weiner process. This is a bit trickier to derive and I can't find a simple derivation to point you to, so I typed one up quickly. Also see: https://en.wikipedia.org/wiki/Wiener_process#Running_maximumand http://math.stackexchange.com/questions/946968/law-of-a-geometric-brownian-motion-first-hitting-time-proof-checking?rq=1(though note there's a mistake in the latter) Hope this helps, Michael On Tue, Nov 24, 2015 at 7:23 PM, Michael Weylandt <[hidden email]> wrote: > On Tue, Nov 24, 2015 at 6:31 PM, Nick White <[hidden email]> wrote: >> You might want to check out the derivation of the Thorp / >> Black-Scholes-Merton formula as it deals with essentially the same >> concepts... >> >> On Wed, Nov 25, 2015 at 11:27 AM, Ernest Stokely <[hidden email]> >> wrote: >> >>> Maybe a naive question but given the price and SD of an asset, is there a >>> way to calculate the probability of hitting a stop set at X over the next N >>> days? I know making appropriate assumptions, this is a Wiener process but >>> can't find the correct equation. >>> >>> A) Is there a closed form solution for this? >>> B) Is there an R function related to this? >>> > > Black-Scholes (and stochastic volatility extensions) can give you a > probability of hitting a price under the equivalent martingale measure > ("Q") but that can be pretty far from the "real-world" ("P") > probability of the same event happening. Or it may be close, depends > on your market. > > If you don't want to do the math (it really is easy though -- half a > page at most), the relevant delta is decent approximation. _______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance-- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go. WP_RunningMax.pdf (130K) Download Attachment