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中文摘要：
综合应用Δ对冲技巧以及Ito引理,在风险中性意义的前提下建立了房产开发商＂降价补差＂承诺期权的偏微分方程定价模型.根据＂降价补差＂承诺能否在到期前任何一天履约,分别建立了欧式承诺期权定价模型和美式承诺期权定价模型.对于欧式承诺期权,得到了期权价格的解析公式;对于美式承诺期权,采用基于自适应的有限差分法对上述定价模型进行数值计算,得到了相应的期权价格.并以欧式承诺期权为例,分析了期权价格对参数的依赖关系.最后对两个具体的＂降价补差＂承诺期权案例进行了期权价格计算.
英文摘要：
Based on theΔhedging and Ito lemma,apartial differential equation model for a real option of a compensation promise for price reduction was established under the neutral risk assumption.According to the time for honoring the promise,the European option pricing model and the American option pricing model were proposed,respectively.For the European option of the compensation,the option pricing formula can be obtained.For the American option of the compensation,the option price can be obtained by using a finite difference scheme based on the layer adapted grid.The relationship between the option price and the parameters of the option pricing model was analyzed.Finally,option prices were calculated for two cases.
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