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. This presentation is based on a joint work with Christa Cuchiero and Sara Svaluto-Ferro.
Guido is a final-year PhD student in the Institute of Statistics and Operations Research at the University of Vienna, jointly supervised by Professor Christa Cuchiero and Professor Irene Klein. He graduated in Mathematics at the University of Turin in 2019, after writing his master thesis with Professor Alexandra Carpentier on multi-armed bandits. His research interests include signature methods and their applications to data science and mathematical finance.
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