Understanding the stop-losses: a simple jump model.
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Отправлено Quark, 20:15:44 04/11/2002:

 
(This is my contribution to the discussion at
 
http://www.howtotrade.ru/cgi-bin/forum.cgi?read=0&file=0005
 
Unfortunately, the message is too long to put it there).
 
 
The stop-loss orders are generally used for reducing the undertaken risk at the financial market. But that is not a complete story. To understand, how one can possibly profit by correct placing of stop-loss, let us consider the jump model of behaviour of logarithmic price increment C(t) = log(P(t+1)/P(t)):
 
 
C(t) = alpha + g(t) + z(t)*J(t)
 
 
where alpha is constant (trend), g(t) is zero mean Gaussian noise with some small variance sigma, J(t) is a JUMP term with large (possibly infinite) variance and unknown (nonGaussian) but almost symmetric distribution. z(t) is 1 with probability p, and 0 with (1-p), where p is somewhat close to zero.  
 
 
In this model J(t) describes sudden price jumps due to various factors (e.g. arriving news, unpredictable events, market games, investors clustering, etc.). z(t) is (switch on/switch off) term, which is usually equal to zero (price jumps are rare). When there are no price jumps (z=0), the price is governed by simple Brownian motion g(t).
 
 
Correct putting of stop-loss order would imply the following requirements: 1) It should not be reached by Brownian motion g(t), i.e. delta_stop_loss is considerably more than sigma.
 
2) It should restrict the losses due to price jumps, i.e. delta_stop_loss is significantly less than the expected jumps. We suppose that the stock is sufficently liquid and there is no slippery.
 
 
If we are successful in implementing the requirements 1-2, we get the  profit due to price jumps even if there is no trend (alpha =0).
 
 
The practical receipt of calculating the stop-loss level was given at http://www.howtotrade.ru/archive/9680.shtml
 
 
I would be very grateful for any comments.
 
 
Regards
 


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