Application of Markov Chains in Stock Market

Application of Markov Chains in Stock Market

In Our Last Chapter, We have discussed about Stochastic Modeling in Stock Market.

A Markov model is a stochastic model used to model pseudo-randomly changing systems. There are 4 types of Markov Model. Let’s start by naively describing how the simplest model among those, Markov Chain works. We shall revisit the concept of Markov Model in detail in later.

The States of a Markov Chain

Lets start with an example of NIFTY. Tomorrow, NIFTY can have three states –

• It can either end in green.
• It can either end in red.
• It is in the same place.

Note – On any given day, NIFTY will be following one of these three states. Now, as per the theory of the Markov Chain, We need to assume that, tomorrow’s state of NIFTY depends on today’s state.

So, What happens today is dependant on yesterday’s state and so on!

In other words – There is a way to predict what will be the state of NIFTY tomorrow if you know the state of NIFTY today.

Example of a Markov Chain in Stock Market

For example –

Tomorrow, there is 60% chance NIFTY’s state (By state in this context we mean NIFTY will close in) will be `Upside` given that today its state is `Downside`. We are using the term `State` because that is the convention.

Let’s represent this in the diagram in weighted arrows. The arrow originates from the current state and points to the future state.

Another –

Let’s say, there is a 20% chance that tomorrow, NIFTY’s state will be `Upside` again if today its state is `Upside`.

You can see it is represented with a Self Pointing arrow.

Each arrow is called a transition from one state to another. In the diagram here, You can see all the possible transitions. This diagram is called `Markov Chain`.

Pseudo-randomness –

Markov Models are used to explain random processes that depend on their current state. So, they characterize processes that are not completely random and independent.  That’s why the term `Psuedo-random` is used in the definition.

Note on Probability Theory –

The sum of the weights of the outgoing arrows from any state is 1. This has to be true because they represent probabilities and for probabilities to make sense, they must add up to 1. Now, there are some special cases of Markov chains but We are not extending our discussion there for now.

The Markov Property - Memory Less Function

The Markov property means that the evolution of the Markov process in the future depends only on the present state and does not depend on past history.

The Markov process does not remember the past if the present state is given.  Hence, the Markov process is called the process with memoryless property.

Example –

Suppose Nifty was up in `x1` day, down in `x2` day, down in `x3` day, neutral in `x4` day. How we should determine the probability that the state of `x5` day will be up? (`x1,x2,x3,x4` are assumed to be consecutive four trading days. And, by neutral, We meant consolidation phase.)

As per Markov Property, to get the state of `x5` day, We need to know the state of `x4` day. If you see the diagram of the Markov Chain above, the answer is 50%.