# [R-SIG-Finance] Computing stop probability

Michael Weylandt michael.weylandt at gmail.com
Wed Nov 25 04:39:24 CET 2015

```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
<michael.weylandt at gmail.com> wrote:
> On Tue, Nov 24, 2015 at 6:31 PM, Nick White <n-e-w at qtradr.net> 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 <wizardchef at gmail.com>
>> 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
>
> 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.
-------------- next part --------------
A non-text attachment was scrubbed...
Name: WP_RunningMax.pdf
Type: application/pdf
Size: 97446 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/r-sig-finance/attachments/20151124/f2bb76e0/attachment.pdf>
```