We consider a market that consists of a dividend-paying stock and a risk-free asset. Then we generalize the model above to n periods. The time interval [0,T] is discretize to T={it:i=0,1,2,,n} with t=T. The rate of return of the risk-free asset in each period is rt. And the rate of dividend of the stock is qt, i.e., for any tT, stock holders can received qSlt of dividends per share at time t+t. And for any tT, St+t={uSt,dSt,withprobabilityp,withprobabilityq. Suppose we have an option written on the stock with payoff VT that is a function of (St)tT. Does there exist a strategy of trading the stock and risk-free asset that can replicate the option payoff VT ? Find a formula for the no-arbitrage option price in terms of a mathematical expectation of the discounted payoff (1+rt)nVT under a probability measure