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摘要翻译：
当资产服从Dupire型局部波动率模型时，我们得到了未定权益的新的封闭形式定价公式。为了得到公式，我们使用了我们最近在[5,6,8]中对热核的短时渐近展开所发展的Dyson-Taylor交换子方法，得到了定价核和导数价格的一族一般闭式近似解。引导方案允许我们将我们的方法扩展到大时间。我们还进行了解析和数值误差分析，并将我们的结果与其他已知的方法进行了比较。
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英文标题：
《Closed form asymptotics for local volatility models》
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作者：
Wen Cheng, Nick Costanzino, John Liechty, Anna Mazzucato, Victor
Nistor
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最新提交年份：
2010
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
We obtain new closed-form pricing formulas for contingent claims when the asset follows a Dupire-type local volatility model. To obtain the formulas we use the Dyson-Taylor commutator method that we have recently developed in [5, 6, 8] for short-time asymptotic expansions of heat kernels, and obtain a family of general closed-form approximate solutions for both the pricing kernel and derivative price. A bootstrap scheme allows us to extend our method to large time. We also perform analytic as well as a numerical error analysis, and compare our results to other known methods.
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PDF链接：
https://arxiv.org/pdf/0910.2309
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