英文标题：
《Higher order approximation of call option prices under stochastic
volatility models》
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作者：
Archil Gulisashvili, Ra\\\'ul Merino, Marc Lagunas and Josep Vives
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最新提交年份：
2019
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英文摘要：
In the present paper, a decomposition formula for the call price due to Al\\`{o}s is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Al\\`{o}s, Gatheral and Radoi\\v{c}i\\\'{c}. We use the new decomposition to obtain various approximations to the call price in the Heston model with sharper estimates of the error term than in the previously known approximations. One of the formulas obtained in the present paper has five significant terms and an error estimate of the form $O(\\nu^{3}(\\left|\\rho\\right|+\\nu))$, where $\\nu$ is the vol-vol parameter, and $\\rho$ is the correlation coefficient between the price and the volatility in the Heston model. Another approximation formula contains seven more terms and the error estimate is of the form $O(\\nu^4(1+|\\rho|)$. For the uncorrelated Hestom model ($\\rho=0$), we obtain a formula with four significant terms and an error estimate $O(\\nu^6)$. Numerical experiments show that the new approximations to the call price perform especially well in the high volatility mode.
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中文摘要：
本文将Al`{o}s引起的买入价分解公式转化为含有随机项的无穷级数的Taylor型公式。新的分解可以被认为是Al`{o}s、Gatheral和Radoi\\v{c}i\\{c}最近的一篇论文中发现的买入价分解的替代方法。我们使用新的分解来获得赫斯顿模型中买入价格的各种近似值，与之前已知的近似值相比，误差项的估计值更精确。本文得到的其中一个公式有五个有效项，误差估计形式为$O（\\ nu ^{3}（\\ left | \\ rho \\ right |+\\ nu））$，其中$\\ nu$是vol-vol参数，$\\ rho$是赫斯顿模型中价格与波动率之间的相关系数。另一个近似公式包含七个以上的项，误差估计的形式为$O（\\nu^4（1+）\\rho |）$。对于不相关的Hestom模型（$\\rho=0$），我们得到了一个包含四个有效项的公式和一个错误估计值$O（\\nu^6）$。数值实验表明，新的看涨期权价格近似方法在高波动模式下表现得尤其好。
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分类信息：

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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