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假设股票变化过程服从跳一分形布朗运动,根据风险中性定价原理对股票发生跳跃次数的收益求条件期望现值推导出M次离散支付红利的美式看涨期权解析定价方程,并使用外推加速法求出当M趋于无穷时方程的二重、三重正态积分多项式表达,依此计算连续支付红利美式看涨期权价值.数值模拟表明通常仅需二重正态积分多项式能产生精确价值,而在极实值状态下则需三重正态积分多项式才能满足,结合两种多项式可以编出有效数字程序评价支付红利的美式看涨期权.
Assuming that the process of stock change obeys the jump-fractal Brownian motion, according to the risk-neutral pricing principle, the expected value of the yield of the number of jumps in the stock is obtained and the American call option pricing equation of M discrete disbursements is deduced. We get the expression of double and triple normal integral polynomials when M tends to infinity and calculate the value of continuous pay dividend American call option.Numerical simulation shows that normally only the double normal integral polynomial can produce precise value, In the very real state, a triple normal-integral polynomial is required to satisfy. Combining the two polynomials, an American call option that evaluates the dividend effectively can be compiled.