École Nationale Supérieure de
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Résumé

The rough path theory is a non-linear extension of the classical theory of controlled differential equations. The most important object in the Rough path theory is the signature of a path. It is rich enough to approximate any function of the path up to any given precision by the use of a linear combination of its components. Applied to finance, we show that we can compute efficiently and with high accuracy the price of options under some continuity conditions by the use of the signature of a stochastic process, which can be developed as a fast and accurate substitute of a classic Monte Carlo simulation. The plus-value of the signature method is its capacity to be model-free and its capacity to price large baskets of options in less time. Time optimization exactly occurs when working with different models or when pricing different options in the same model. We focus on the Black-Sholes model in the case of one risky asset and 2 risky assets, but the approach described in this paper is valid for any time-homogenous Ito diffusion process. This framework covers European options, Asian options, lookback with floating strike options, spread options.

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• Option Pricing using the Signature of a Stochastic Process (deposited 05 juin 2023 14:46) [Actuellement Affiché]