Consider the particular (binary options pricing model) three-period model with S₀ = $4 (initial stock price), u = 2 (factor it can grow), d = 1/2 (factor it can shrink) , and R = 1 + 1/4 (the interest rate per period, here 25%). At time 1, the stock price S₁ can be either 2 or 8, at time 2, S₂ is 1,4, or 16, at time 3, S₃ is either 0.5, 2, 8 or 32.

Consider a European put option with strike price K = $4. Explain the dynamic hedging strategy, work out the (re-adjusted) portfolio values (i.e. the dollar amount of stocks and bonds) at each time and for each movement of the stock price.

What is the no-arbitrage price for the option at time 0?