Let us consider a European-style call option on an underlying stock share whose price dynamics is represented by a three-step binomial lattice.

The lattice has 4 nodes in the last time layer, corresponding to maturity). Timeto-maturity is one year, and the continuously compounded (annual) risk-free rate is 3%. The current underlying asset price is  \($30\) and the strike is  \($30.\) We do not consider dividends and, at each time step, the stock share either gains 15%, with probability 0.6, or loses 10%, with probability 0.4. Price the option. Consider the sample path (up, up, down), and imagine that we are at the beginning of the last time period (after two steps, when time-to-maturity is four months). How many stock shares should be bought or sold (at this time instant) by the option writer to hedge risk?