英文标题：
《Arbitrage-free prediction of the implied volatility smile》
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作者：
Petros Dellaportas, Aleksandar Mijatovi\\\'c
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最新提交年份：
2014
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英文摘要：
  This paper gives an arbitrage-free prediction for future prices of an arbitrary co-terminal set of options with a given maturity, based on the observed time series of these option prices. The statistical analysis of such a multi-dimensional time series of option prices corresponding to $n$ strikes (with $n$ large, e.g. $n\\geq 40$) and the same maturity, is a difficult task due to the fact that option prices at any moment in time satisfy non-linear and non-explicit no-arbitrage restrictions. Hence any $n$-dimensional time series model also has to satisfy these implicit restrictions at each time step, a condition that is impossible to meet since the model innovations can take arbitrary values. We solve this problem for any $n\\in\\NN$ in the context of Foreign Exchange (FX) by first encoding the option prices at each time step in terms of the parameters of the corresponding risk-neutral measure and then performing the time series analysis in the parameter space. The option price predictions are obtained from the predicted risk-neutral measure by effectively integrating it against the corresponding option payoffs. The non-linear transformation between option prices and the risk-neutral parameters applied here is \\textit{not} arbitrary: it is the standard mapping used by market makers in the FX option markets (the SABR parameterisation) and is given explicitly in closed form. Our method is not restricted to the FX asset class nor does it depend on the type of parameterisation used. Statistical analysis of FX market data illustrates that our arbitrage-free predictions outperform the naive random walk forecasts, suggesting a potential for building management strategies for portfolios of derivative products, akin to the ones widely used in the underlying equity and futures markets.
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中文摘要：
本文基于观察到的期权价格时间序列，对给定到期日的任意共终端期权集的未来价格进行了无套利预测。由于期权价格在任何时刻都满足非线性和非显式无套利限制，因此，对与$n$敲打（具有$n$大，例如$n\\geq 40$）和相同到期日相对应的期权价格的多维时间序列进行统计分析是一项困难的任务。因此，任何$n$维时间序列模型也必须在每个时间步满足这些隐式限制，这是一个不可能满足的条件，因为模型创新可以采用任意值。我们首先根据相应风险中性度量的参数对每个时间步的期权价格进行编码，然后在参数空间中执行时间序列分析，从而解决了外汇（FX）中任何$n\\in\\NN$的问题。通过有效地将预测的风险中性度量与相应的期权收益相结合，可以从预测的风险中性度量中获得期权价格预测。期权价格和此处应用的风险中性参数之间的非线性转换是任意的：它是外汇期权市场中做市商使用的标准映射（SABR参数化），并以封闭形式明确给出。我们的方法不仅限于外汇资产类别，也不取决于使用的参数化类型。对外汇市场数据的统计分析表明，我们的无套利预测优于天真的随机游走预测，这表明有可能为衍生产品投资组合建立管理策略，类似于在基础股票和期货市场广泛使用的策略。
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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：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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