You have a contract called an option to purchase a share of stock when you desire, at

Question:

You have a contract called an option to purchase a share of stock when you desire, at the fixed price of 3 monetary units. The day-today price of the stock follows a Markov chain with the transition diagram below. If the option is exercised when the price is \(s\), then the stock can be immediately resold at a profit of \(s-3\). You do not have to exercise the option at all if it is not beneficial, but note that there is a chance that the company will go bankrupt before the option is exercised if you wait too long, in which case it will be worthless. When should you exercise the option?

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