DeepAI AI Chat
Log In Sign Up

Non-Equilibrium Skewness, Market Crises, and Option Pricing: Non-Linear Langevin Model of Markets with Supersymmetry

by   Igor Halperin, et al.

This paper presents a tractable model of non-linear dynamics of market returns using a Langevin approach.Due to non-linearity of an interaction potential, the model admits regimes of both small and large return fluctuations. Langevin dynamics are mapped onto an equivalent quantum mechanical (QM) system. Borrowing ideas from supersymmetric quantum mechanics (SUSY QM), we use a parameterized ground state wave function (WF) of this QM system as a direct input to the model, which also fixes a non-linear Langevin potential. A stationary distribution of the original Langevin model is given by the square of this WF, and thus is also a direct input to the model. Using a two-component Gaussian mixture as a ground state WF with an asymmetric double well potential produces a tractable low-parametric model with interpretable parameters, referred to as the NES (Non-Equilibrium Skew) model. Supersymmetry (SUSY) is then used to find time-dependent solutions of the model in an analytically tractable way. The model produces time-varying variance, skewness and kurtosis of market returns, whose time variability can be linked to probabilities of crisis-like events. For option pricing out of equilibrium, the NES model offers a closed-form approximation by a mixture of three Black-Scholes prices, which can be calibrated to index options data and used to predict moments of future returns. The NES model is shown to be able to describe both regimes of a benign market and a market in a crisis or a severe distress.


page 1

page 2

page 3

page 4


Financial Market Modeling with Quantum Neural Networks

Econophysics has developed as a research field that applies the formalis...

Pricing under a multinomial logit model with non linear network effects

We study the problem of pricing under a Multinomial Logit model where we...

Certification Design for a Competitive Market

Motivated by applications such as voluntary carbon markets and education...

Option Volume Imbalance as a predictor for equity market returns

We investigate the use of the normalized imbalance between option volume...

Reputation and Pricing Dynamics in Online Markets

We study the economic interactions among sellers and buyers in online ma...

Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning

We consider the problem of simultaneously approximating the conditional ...

How rarity shapes the NFT market

We quantify Non Fungible Token (NFT) rarity and investigate how it impac...