American Call Pricing on Dividend-Paying and Placing Stocks with Stochastic Volatility

We derive the law of stock price with dividend-paying and placing, and discuss the problem of option pricing on dividend-paying and placing stocks with stochastic volatility. It is concluded by the discussion of American option with convex paying function, that the optimal exercising time of American call options can only be at the time immediately before payment of the dividend or expiration time. We also give the stochastic differential equation of the value function of the option.