英文标题：
《Anomalous diffusions in option prices: connecting trade duration and the
  volatility term structure》
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作者：
Antoine Jacquier and Lorenzo Torricelli
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最新提交年份：
2020
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英文摘要：
  Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to different distribution spread rates compared to standard models. In financial modelling this has been used to accommodate for random trade duration in the tick-by-tick price process. We show here that anomalous diffusions are able to reproduce the market behaviour of the implied volatility more consistently than usual L\\\'evy or stochastic volatility models. We focus on two distinct classes of underlying asset models, one with independent price innovations and waiting times, and one allowing dependence between these two components. These two models capture the well-known paradigm according to which shorter trade duration is associated with higher return impact of individual trades. We fully describe these processes in a semimartingale setting leading no-arbitrage pricing formulae, and study their statistical properties. We observe that skewness and kurtosis of the asset returns do not tend to zero as time goes by. We also characterize the large-maturity asymptotics of Call option prices, and find that the convergence rate is slower than in standard L\\\'evy regimes, which in turn yields a declining implied volatility term structure and a slower decay of the skew.
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中文摘要：
反常扩散是连续时间随机游动的标度极限，其创新时间按幂律分布。与标准模型相比，非指数等待时间的影响不会随时间而消失，并导致不同的分布扩散率。在金融建模中，这被用来适应逐点定价过程中的随机交易持续时间。我们在此表明，异常扩散能够比通常的列维或随机波动率模型更一致地再现隐含波动率的市场行为。我们关注两类不同的基础资产模型，一类具有独立的价格创新和等待时间，另一类允许这两个组成部分之间的依赖性。这两个模型抓住了众所周知的范式，即交易持续时间越短，单个交易的回报影响越大。我们在半鞅环境下充分描述了这些过程，导出了无套利定价公式，并研究了它们的统计性质。我们观察到，随着时间的推移，资产回报的偏度和峰度并不趋于零。我们还描述了看涨期权价格的大成熟度渐近性，并发现收敛速度比标准列维制度慢，这反过来会导致隐含波动率期限结构的下降和偏斜的缓慢衰减。
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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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