Computing stop probability
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
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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