英文标题：
《Vanna-Volga Method for Normal Volatilities》
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作者：
Volodymyr Perederiy
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最新提交年份：
2020
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英文摘要：
  Vanna-Volga is a popular method for the interpolation/extrapolation of volatility smiles. The technique is widely used in the FX markets context, due to its ability to consistently construct the entire Lognormal smile using only three Lognormal market quotes. However, the derivation of the Vanna-Volga method itself is free of distributional assumptions. With this is mind, it is surprising there have been no attempts to apply the method to Normal volatilities (the current standard for interest rate markets). We show how the method can be modified to build Normal volatility smiles. As it turns out, only minor modifications are required compared to the Lognormal case. Moreover, as the inversion of Normal volatilities from option prices is easier in the Normal case, the smile construction can occur at a machine-precision level using analytical formulae, making the approximations via Taylor-series unnecessary. Apart from being based on practical and intuitive hedging arguments, the Vanna-Volga has further important advantages. In comparison to the Normal SABR model, the Vanna-Volga can easily fit both classical convex and atypical concave smiles (frowns). Concave smile patterns are sometimes observed around ATM strikes in the interest rate markets, particularly in the situations of anticipated jumps (with an unclear outcome) in interest rates. Besides, concavity is often observed towards the lower/left end of the Normal volatility smiles of interest rates. At least in these situations, the Vanna-Volga can be expected to interpolate/extrapolate better than SABR.
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中文摘要：
Vanna-Volga是波动率微笑插值/外推的常用方法。该技术在外汇市场中得到了广泛应用，因为它能够仅使用三个对数正态市场报价来持续构建整个对数正态微笑。然而，Vanna-Volga方法的推导本身没有分布假设。考虑到这一点，令人惊讶的是，没有人试图将该方法应用于正常波动率（利率市场的现行标准）。我们展示了如何修改该方法以构建正常的波动率微笑。事实证明，与对数正态分布情况相比，只需要稍作修改。此外，由于在正常情况下更容易从期权价格中反演正常波动率，因此可以使用分析公式在机器精度水平上进行微笑构造，从而不需要通过泰勒级数进行近似。除了基于实际和直观的对冲论点外，瓦纳伏尔加还有其他重要优势。与正常的SABR模型相比，Vanna-Volga可以很容易地拟合经典的凸面笑容和非典型的凹面笑容（皱眉）。在利率市场中，有时会观察到ATM罢工周围的凹形微笑模式，特别是在利率预期跳跃（结果不明确）的情况下。此外，在利率正常波动率微笑的下端/左端经常观察到凹面。至少在这些情况下，Vanna-Volga可以比SABR更好地进行插值/外推。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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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