Computing stop probability

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Computing stop probability

wizardchef1
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

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Re: Computing stop probability

Nick-2
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.
>

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Re: Computing stop probability

Michael Weylandt
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.

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Re: Computing stop probability

Rex-2
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-3


Note 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.

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Re: Computing stop probability

Michael Weylandt
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_maximum
and 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.

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