论文标题
基于签名的模型：理论和校准
Signature-based models: theory and calibration
论文作者
论文摘要
我们考虑了资产价格模型，其动力学是通过（时间扩展）签名的主要基础过程的线性函数来描述的，该过程的范围从（市场上的）布朗运动到一般的多维连续连续半段。该框架是通用的，从某种意义上说，经典模型可以任意地近似，并且可以通过简单的方法从可用数据的所有来源中学习该模型的参数。我们提供的条件可以保证缺乏套利以及可用于所谓的Sig-Payoffs的可容纳选项定价公式，从而利用了通用主要过程的多项式性质。我们的主要重点之一在于校准，在该校准中，我们考虑了时间序列和隐含的波动表面数据，该数据是由经典随机波动率模型以及S＆P500指数市场数据产生的。对于这两项任务，模型的线性性都是至关重要的障碍功能，可以获得快速，准确的校准结果。
We consider asset price models whose dynamics are described by linear functions of the (time extended) signature of a primary underlying process, which can range from a (market-inferred) Brownian motion to a general multidimensional continuous semimartingale. The framework is universal in the sense that classical models can be approximated arbitrarily well and that the model's parameters can be learned from all sources of available data by simple methods. We provide conditions guaranteeing absence of arbitrage as well as tractable option pricing formulas for so-called sig-payoffs, exploiting the polynomial nature of generic primary processes. One of our main focus lies on calibration, where we consider both time-series and implied volatility surface data, generated from classical stochastic volatility models and also from S&P500 index market data. For both tasks the linearity of the model turns out to be the crucial tractability feature which allows to get fast and accurate calibrations results.
