Quant Interview Practice Questions

Consider a simplified model of a stock's price movement, represented as a two-state Markov chain: State A (high price) and State B (low price). The probability of transitioning from State A to State B is 0.3, and the probability of transitioning from State B to State A is 0.5. Assuming this Markov chain reaches a stationary distribution, what is the probability of the stock being in State A?