Regensburg 2022 – wissenschaftliches Programm

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 4: Financial Risk

SOE 4.1: Vortrag

Montag, 5. September 2022, 12:00–12:15, H11

From many-body physics to financial markets: sparse modeling for inverse problems — •Daniel Guterding — Fachbereich Mathematik, Naturwissenschaften und Datenverarbeitung, Technische Hochschule Mittelhessen, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany

The accurate valuation of plain-vanilla derivatives is one of the fundamental tasks of mathematical finance. In particular, arbitrage-free interpolations of market-quoted option prices or implied volatilities are needed for the pricing of most options. For this purpose, various standard interpolation techniques have been modified to accommodate the no-arbitrage conditions required by quantitative finance.

Despite this problem being so important for option pricing, the available approaches are quite involved and largely not stable against the noisy inputs that are often encountered in practical applications. Making use of recent progress on inverse problems in many-body physics [1], our method [2] is based on the relation between the terminal density of the underlying asset and plain-vanilla option prices.

We construct a few-parameter model for this relation using the singular value decomposition, which obviates the need to explicitly choose expansion or regression basis functions, such as they are encountered in many other methods. Furthermore, we show that our method by construction delivers arbitrage-free models even for inputs containing noise or severe arbitrage.

[1] Otsuki et al., J. Phys. Soc. Japan 89, 012001 (2020)

[2] Guterding, arXiv:2205.10865