This paper studies the valuation and optimal exercise time of American call option on stock whose price process is modelled by dividends discount model, namely the net present value of all its future discrete dividend payments. Under the assumption that the dividend process subjects to exponential Levy process, this paper strictly proves that the discount process of the stock price is a martingale. By applying the reverse recursively analysis techniques and constructing a series of European call options, this paper piecewise derives the valuation of American call option at any time and gives the optimal exercise time.
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