Automated Option Pricing: Numerical Methods
Automated Option Pricing: Numerical Methods
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自动期权定价：数值方法
DOI：
10.2139/ssrn.1968344
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Henry
中科院分区：
文献类型：
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作者：
P. Henry
在本文中，我们研究了给定一组市场工具的期权价格与模型无关的界限。这个超级复制问题可以写成半无限线性规划问题。由于这些超级复制价格可能很大，并且达到上限的密度 ℚ 非常单一，因此我们限制 ℚ 在熵意义上接近下一阶段的先验概率度量。这导致了我们的风险中性加权蒙特卡罗方法，该方法与约束凸问题相关。我们解释了如何使用割平面法中的原始对偶内点算法和拟牛顿算法有效地解决这些大规模问题。各种例子说明了这些算法的效率和广泛的适用性。
In this paper, we investigate model-independent bounds for option prices given a set of market instruments. This super-replication problem can be written as a semi-infinite linear programing problem. As these super-replication prices can be large and the densities ℚ which achieve the upper bounds quite singular, we restrict ℚ to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral weighted Monte Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.