Foreign Exchange Market Microstructure and the WM/Reuters 4pm Fix

A market fix serves as a benchmark for foreign exchange (FX) execution, and is employed by many institutional investors to establish an exact reference at which execution takes place. The currently most popular FX fix is the World Market Reuters (WM/R) 4pm fix. Execution at the WM/R 4pm fix is a service offered by FX brokers (normally banks), who deliver execution at the fix provided they obtain the trade order until a certain time prior to 4pm. In this paper, we study the market microstructure around 4pm. We demonstrate that market dynamics can be distinguished from other times during the day through increased volatility and size of movements. Our findings question the aggregate benefit to the client base of using the 4pm fix in its current form.Comment: 20 Pages, 6 Figures, 3 Table

The Effect of Non-Smooth Payoffs on the Penalty Approximation of American Options

This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the literature, sharp rates of convergence and particularly the effect of gradient discontinuities (i.e., the omni-present `kinks' in option payoffs) on this rate have not been fully analysed so far. This effect becomes important not least when using penalisation as a numerical technique. We use matched asymptotic expansions to characterise the boundary layers between exercise and hold regions, and to compute first order corrections for representative payoffs on a single asset following a diffusion or jump-diffusion model. Furthermore, we demonstrate how the viscosity theory framework in [Jakobsen, 2006] can be applied to this setting to derive upper and lower bounds on the value. In a small extension to [Bensoussan & Lions, 1982], we derive weak convergence rates also for option sensitivities for convex payoffs under jump-diffusion models. Finally, we outline applications of the results, including accuracy improvements by extrapolation.Comment: 34 Pages, 10 Figure

Introducing a new Workflow for Pig Posture Classification based on a combination of YOLO and EfficientNet

This paper introduces a pipeline for image-based pig posture classification by applying YOLOv5 for pig detection and EfficientNet for subsequent pig posture classification into 'lying' and 'notLying'. A high-quality dataset consisting of 5311 heterogeneous images from different sources with 78215 bounding box annotations was created. The bounding box annotations were then used to create a separate dataset for image classification, consisting of 9209 and 7855 images for each 'lying' and 'notLying'. The YOLOv5 model achieves an AP of 0.994 for pig detection, while EfficientNet achieves a precision of 0.93 for pig posture classification. Comparing the results of the proposed method with other approaches found in literature, it shows that significant improvements in terms of accuracy can be achieved by splitting the classification of pig posture into separate models. This research provides a foundation for the continued development of real-time monitoring and assistance systems in pig Precision Livestock Farming

Numerical Solution of Discretised HJB Equations with Applications in Finance

tesis no hubiese sido posible. Muchísimas gracias, amigo. Simplicity is the keynote of all true elegance

On the Use of Policy Iteration as an Easy Way of Pricing American Options

In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [Forsyth & Labahn, 2007], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American options. We show that, in general, O(N) is an upper and lower bound on the number of iterations needed to solve a discrete LCP of size N. If embedded in a class of standard discretisations with M time steps, the overall complexity of American option pricing is indeed only O(N(M+N)), and, therefore, for M N, identical to the pricing of European options, which is O(MN). We also discuss the numerical properties and robustness with respect to model parameters in relation to penalty and projected relaxation methods.