Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization

Generalized Arbitrage-Free SVI Volatility Surfaces

In this article we propose a generalisation of the recent work of Gatheral-Jacquier [11] on explicit arbitrage-free parameterisations of implied volatility surfaces. We also discuss extensively the notion of arbitrage freeness and Roger Lee’s moment formula using the recent analysis by Roper [18]. We further exhibit an arbitrage-free volatility surface different from Gatheral’s SVI parameterisa...

From arbitrage to arbitrage-free implied volatilities

We propose a method for determining an arbitrage-free density implied by the Hagan formula. (We use the wording “Hagan formula” as an abbreviation of the Hagan– Kumar–Leśniewski–Woodward model.) Our method is based on the stochastic collocation method. The principle is to determine a few collocation points on the implied survival distribution function and project them onto the polynomial of an ...

Arbitrage-free pricing of XVA

Energy Storage Arbitrage in Real-Time Markets Via Reinforcement Learning

In this paper, we derive a temporal arbitrage policy for storage via reinforcement learning. Real-time price arbitrage is an important source of revenue for storage units, but designing good strategies have proven to be difficult because of the highly uncertain nature of the prices. Instead of current model predictive or dynamic programming approaches, we use reinforcement learning to design a ...

Machine Learning in Statistical Arbitrage

We apply machine learning methods to obtain an index arbitrage strategy. In particular, we employ linear regression and support vector regression (SVR) onto the prices of an exchange-traded fund and a stream of stocks. By using principal component analysis (PCA) in reducing the dimension of feature space, we observe the benefit and note the issues in application of SVR. To generate trading sign...