Stock traders pay close attention to the \"ticks\" of a stock. A stock can trade

Question

Stock traders pay close attention to the "ticks" of a stock. A stock can trade on an uptick, even tick, or downtick, if the trade price is higher, the same MCS-3 LIMITING STATE PROBABILITIES FOR A FINITE MARKOV CHAIN 10 or lower than the previous trade price. For a particular stock, traders have observed that the ticks are accurately modeled by a Markov chain. Following an even tick, the next trade is an even tick with probability 0.6, an uptick with probability 0.2, or a downtick with probability 0.2. After a downtick another downtick has probability 0.4, while an even tick has probability 0.6 After an uptick, another uptick occurs with probability 0.4, while an even tick occurs with probability 0.6. Using states 0, 1,2 to denote the previous trade being a downtick, an even tick, or an uptick, sketch the Markov chain and find the state transition matrix P and the n-step transition matrix P

Explanation / Answer

Ans:Transition probability matrix P:

n-step transition probability matrix is given by: Pn

It is used to find out the distribution vector after nth step,if we know the intial distribution vector a0.

an=a0*Pn

0(downtick) 1(eventick) 2(uptick) 0(downtick) 0.4 0.6 0 1(eventick) 0.2 0.6 0.2 2(uptick) 0 0.6 0.4

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