英文标题：
《Closed-form approximations with respect to the mixing solution for
option pricing under stochastic volatility》
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作者：
Kaustav Das and Nicolas Langren\\\'e
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最新提交年份：
2021
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英文摘要：
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion around the mean of its argument. The difficulties then faced are simplifying a number of expectations induced by the Taylor expansion. Under the assumption of piecewise-constant parameters, we derive closed-form pricing formulas and devise a fast calibration scheme. Furthermore, we perform a numerical error and sensitivity analysis to investigate the quality of our approximation and show that the errors are well within the acceptable range for application purposes. Lastly, we derive bounds on the remainder term generated by the Taylor expansion.
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中文摘要：
我们考虑了具有时间相关参数的Heston和GARCH扩散随机波动率模型中欧式看跌期权价格的闭合形式近似。我们的方法包括将看跌期权价格写成布莱克-斯科尔斯公式的期望值，并围绕其参数的平均值进行二阶泰勒展开。当时面临的困难是简化了泰勒展开式所带来的许多期望。在分段常数参数的假设下，我们推导了闭式定价公式，并设计了一种快速校准方案。此外，我们还进行了数值误差和灵敏度分析，以研究近似值的质量，并表明误差在应用目的的可接受范围内。最后，我们推导了泰勒展开生成的余项的界。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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