Signature-based models: theory and calibration
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...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
26.07.2022
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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DOI: | 10.48550/arxiv.2207.13136 |