英文标题：
《Switching to non-affine stochastic volatility: A closed-form expansion
for the Inverse Gamma model》
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作者：
Nicolas Langren\\\'e, Geoffrey Lee, Zili Zhu
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最新提交年份：
2016
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英文摘要：
This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=\\kappa_{t}\\left(\\theta_{t}-V_{t}\\right)dt+\\lambda_{t}V_{t}dB_{t}$. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, even though both are as parsimonious (only four stochastic parameters). Indeed, it provides more realistic volatility distribution and volatility paths, which translate in practice into more robust calibration and better hedging accuracy, explaining its popularity among practitioners. In order to price vanilla options with IGa volatility, we propose a closed-form volatility-of-volatility expansion. Specifically, the price of a European put option with IGa volatility is approximated by a Black-Scholes price plus a weighted combination of Black-Scholes greeks, where the weights depend only on the four time-dependent parameters of the model. This closed-form pricing method allows for very fast pricing and calibration to market data. The overall quality of the approximation is very good, as shown by several calibration tests on real-world market data where expansion prices are compared favorably with Monte Carlo simulation results. This paper shows that the IGa model is as simple, more realistic, easier to implement and faster to calibrate than classical transform-based affine models. We therefore hope that the present work will foster further research on non-affine models like the Inverse Gamma stochastic volatility model, all the more so as this robust model is of great interest to the industry.
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中文摘要：
本文介绍了由波动动力学$dV_{t}=\\kappa_{t}\\ left（\\theta_{t}-V_{t}\\ right）dt+\\lambda_{t}V_{t}dB_{t}$定义的具有时变参数的逆伽马（IGa）随机波动模型。这种非仿射模型比经典的仿射模型（如赫斯顿随机波动率模型）更为现实，尽管两者都非常简洁（只有四个随机参数）。事实上，它提供了更现实的波动率分布和波动路径，在实践中转化为更稳健的校准和更好的套期保值准确性，解释了它在从业者中的流行性。为了对具有IGa波动率的普通期权定价，我们提出了波动率扩张的封闭形式波动率。具体而言，具有IGa波动性的欧洲看跌期权的价格由Black-Scholes价格加上Black-Scholes指数的加权组合来近似，其中权重仅取决于模型的四个时间相关参数。这种封闭式定价方法允许非常快速的定价和市场数据校准。近似值的总体质量非常好，在真实市场数据上进行的几次校准测试表明，在这些数据中，扩展价格与蒙特卡罗模拟结果进行了比较。本文表明，IGa模型比经典的基于变换的仿射模型简单、更真实、更容易实现和更快地校准。因此，我们希望，目前的工作将促进对非仿射模型的进一步研究，如逆伽马随机波动率模型，更重要的是，这个稳健的模型是业界非常感兴趣的。
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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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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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