SO I just study the Markov chain which seems to be very powerful tools of what of have learned, So I got the Idea Markov chain only require the repetitive event like if today sunny will tomorrow sunny or the next n period will be sunny.
So I thought of what if I used it in the stock market. But when I start to think of that "ONE THING" is showing up from what the textbook did not tell me.
"IT GIVE THE PROBABILITY RIGHT AWAY" what actually I had read is conditional probability that does not require the probability of that event alone.
So here is what I want to apply and would like you to make a suggestion on whether it works or not.
Use Markov chain for Calculating the risk of investing in one stock ABC, on the probability that whether the next event is UP or DOWN
So Stock market obviously did not provide the probability of Up and Down. So I come up with the counting method
Pr(Up) = N(Up)/N
Pr(Down) = N(Down)/N
Basically, the probability of up is the proportion of event that is up to the total event. same goes for Pr(Down)
In order to do the Markov chain, I need conditional probability.
I hope this is valid as the event is discrete time parameter and this method do not violate the Axioms of probability
Example Event for one month of ABC stock U stands for the closing price of that day is positive D stands for the closing price of that day is negative
Month N : UUUUDDDUUUDUDUUUDUUDDUUUDDDUDU
N(U) = 18 N(D) = 12
P(U) = 18/30 P(D) = 12/30
Now if I want to derive the conditional probability. U,D is no longer U,D it becomes $U_{i}$ $D_{i}$ and i = 1,2,...,30
Recall the conditional probability
Pr(A|B) = Pr(A,B)/Pr(B)
Pr(A, B) = P($U_{i+1}$,$U_{i}$) the joint probability for the event that the in the next day it will increase in price after that it had increased.
So here it starts.
Pr($U_{i+1}$|$U_{i}$) = N($U_{i+1}$,$U_{i}$)/N($U_{i}$) Start counting
N($U_{i+1}$,$U_{i}$) = 10 N($U_{i}$) = 18
Pr($U_{i+1}$|$U_{i}$) = 10/18
So I skipped the counting part so that it is not consumed a lot of space
Pr($U_{i+1}$|$U_{i}$) = 10/18
Pr($D_{i+1}$|$U_{i}$) = 8/18
Pr($U_{i+1}$|$D_{i}$) = 5/12
Pr($D_{i+1}$|$D_{i}$) = 7/12
Now we can draw the transition matrix but I don't know how to do it here, therefore I will just stop here..
Thank you for your support !!!!