FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » Probability
Cumulative Changes Probability
Post new topic   Reply to topic Page 1 of 1 [4 Posts] View previous topic :: View next topic
Author Message
Pavel314
science forum addict


Joined: 29 Apr 2005
Posts: 78

PostPosted: Sun May 07, 2006 1:17 pm    Post subject: Re: Cumulative Changes Probability Reply with quote

"Michael Zedeler" <michael@zedeler.dk> wrote in message
news:oJ67g.162$uS7.137@news.get2net.dk...
Quote:
Pavel314 wrote:
This problem came up during a discussion of trading on the stock market
but the solution probably has wider application. As a disclaimer, I
realize that the past performance of a stock is no indication of future
performance because of many factors in the economy as a whole, and that I
am not looking for a system to beat the market, just a formula to compute
probability.

GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.[...]
The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.

Here is a starting point:

http://en.wikipedia.org/wiki/Black-scholes

Regards,

Michael.


Thank you, that's exactly what I was looking for.

Paul
Back to top
Michael Zedeler
science forum beginner


Joined: 29 Nov 2005
Posts: 17

PostPosted: Sat May 06, 2006 7:23 pm    Post subject: Re: Cumulative Changes Probability Reply with quote

Pavel314 wrote:
Quote:
This problem came up during a discussion of trading on the stock market but
the solution probably has wider application. As a disclaimer, I realize that
the past performance of a stock is no indication of future performance
because of many factors in the economy as a whole, and that I am not looking
for a system to beat the market, just a formula to compute probability.

GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.[...]
The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.

Here is a starting point:

http://en.wikipedia.org/wiki/Black-scholes

Regards,

Michael.
--
Which is more dangerous? TV guided missiles or TV guided families?
Visit my home page at http://michael.zedeler.dk/
Get my vcard at http://michael.zedeler.dk/vcard.vcf
Back to top
Pavel314
science forum addict


Joined: 29 Apr 2005
Posts: 78

PostPosted: Tue May 02, 2006 10:47 am    Post subject: Re: Cumulative Changes Simulation Reply with quote

"Pavel314" <Pavel314@NOSPAM.comcast.net> wrote in message
news:ZLednXWtfoYuXsnZnZ2dnUVZ_sKdnZ2d@comcast.com...
Quote:
This problem came up during a discussion of trading on the stock market
but the solution probably has wider application. As a disclaimer, I
realize that the past performance of a stock is no indication of future
performance because of many factors in the economy as a whole, and that I
am not looking for a system to beat the market, just a formula to compute
probability.

GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.


PROBLEM 1: What is the probability that the stock will have increased in
value at least 10% at the end of the next three weeks, i.e., 15 trading
days? The probability should be given as a function of P, m, s, and 15,
the number of days in the observation period. Where P is the current stock
price and c_i is the change in value for trading day i, I would state the
problem as:

P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P

I've thought about expressing the c_i in terms of confidence intervals but
I get into problems with the summation.


PROBLEM 2: What is the probability that the stock will have increased in
value at least 10% at any time before the end of the next three weeks,
i.e., 15 trading days?

P + c_1 >= 1.1 * P OR
P + c_1 + c_2 >= 1.1 * P OR
P + c_1 + c_2 + c_3 >= 1.1 * P OR
...
P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P


The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.


Since I couldn't solve this problem theoretically, I wrote a Q-Basic program
to simulate the situation under various scenarios. The first parameter is
the value of one standard deviation of the historical daily change as a
percent of the initial stock price. The second works into the two problem
statements above; the first checks to see if the stock has appreciated 10%
at the end of 15 days while the second checks to see if it appreciated 10%
on any day within the 15-day trading period. I ran each of the six scenarios
1,000,000 times; the results are shown below:

StdDev/Price +10% at End of Period +10% Within Period
1% 1,238
1,576
2% 66,772 97,892
4% 238,162 379,117

The moral seems to be that you should take your profit while you can because
there's a significant chance that the stock will go back down.

Paul
Back to top
Pavel314
science forum addict


Joined: 29 Apr 2005
Posts: 78

PostPosted: Sun Apr 30, 2006 2:01 pm    Post subject: Cumulative Changes Probability Reply with quote

This problem came up during a discussion of trading on the stock market but
the solution probably has wider application. As a disclaimer, I realize that
the past performance of a stock is no indication of future performance
because of many factors in the economy as a whole, and that I am not looking
for a system to beat the market, just a formula to compute probability.

GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.


PROBLEM 1: What is the probability that the stock will have increased in
value at least 10% at the end of the next three weeks, i.e., 15 trading
days? The probability should be given as a function of P, m, s, and 15,
the number of days in the observation period. Where P is the current stock
price and c_i is the change in value for trading day i, I would state the
problem as:

P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P

I've thought about expressing the c_i in terms of confidence intervals but I
get into problems with the summation.


PROBLEM 2: What is the probability that the stock will have increased in
value at least 10% at any time before the end of the next three weeks, i.e.,
15 trading days?

P + c_1 >= 1.1 * P OR
P + c_1 + c_2 >= 1.1 * P OR
P + c_1 + c_2 + c_3 >= 1.1 * P OR
...
P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P


The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.

Paul
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [4 Posts] View previous topic :: View next topic
The time now is Sat Aug 19, 2017 1:54 am | All times are GMT
Forum index » Science and Technology » Math » Probability
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts Probability Question dumont Probability 0 Mon Oct 23, 2006 3:38 pm
No new posts probability gorbag Probability 0 Mon Aug 14, 2006 11:06 pm
No new posts Expectation value in terms of cumulative distribution Randy Poe Math 6 Wed Jul 19, 2006 9:34 pm
No new posts Is there a way to write out the process of the cumulative... Michael11 Math 1 Wed Jul 19, 2006 7:16 am
No new posts Probability of attaining a minimum value when rolling dice nick@blackmarble.co.uk Math 16 Tue Jul 18, 2006 2:57 pm

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0777s ][ Queries: 20 (0.0557s) ][ GZIP on - Debug on ]